in this video we're going to talk about how to solve quadratic equations using the quadratic formula so let's start with this one let's say we have the equation 2x squared plus 3x minus 2 is equal to 0. and our goal is to solve for x we want to calculate the value of x that makes this equation true so here is the quadratic formula that we need to use it's negative b plus or minus the square root of b squared minus 4ac divided by 2a now we need to know what a b and c are equal to so in this format where you have all of the x variables to the left and 0 on the right a is the number in front of x squared b is the number in front of x and c is the constant term so this is going to be i'm going to rewrite it here x is equal to negative b b is positive three plus or minus the square root of b squared so that's three squared minus four times a a is two times c which is negative two all divided by two a or two times two so we have negative three plus or minus the square root three squared is nine negative four times two is negative 8 and negative 8 times negative 2 is positive 16. on the bottom we have 2 times 2 which is 4. now 9 plus 16 is 25 and the square root of 25 is 5. so right now that's what we have notice the plus or minus symbol so we need to break this up into two parts so we're going to have negative 3 plus 5 divided by four and negative three minus five divided by four negative three plus five is positive two negative three minus five is negative eight so right now we have two different answers now we can reduce two over four to one over two if you divide both numbers by 2 and 8 divided by 4 is negative 2. so x can equal 1 half or x can equal negative 2. and so that's how you can solve a quadratic equation using the quadratic formula now if you want to check your answer you can plug it in let's plug in negative two into this equation so we have two times negative two squared plus three times minus two minus two let's see if that equals zero negative two squared is negative two times negative two which is four three times negative two is negative six now two times four is eight negative six minus two is negative eight eight minus eight is zero so we know that this answer works and you could try the other one too that's gonna work as well but now let's move on to our next example let's say we have this particular quadratic equation go ahead and use the quadratic formula to get the answer so we can see that a is 6 b is negative 17 and c is 12. so let's begin by writing the formula so it's x is equal to negative b plus or minus the square root of b squared minus 4ac divided by 2a so b is negative 17. and then we have b squared that's negative 17 squared minus four a is six c is 12 divided by two a or two times six so we have negative times negative 17 that becomes positive 17 negative 17 squared is going to be positive 289 and then we have negative 4 times 6 which is negative 24 times 12 that's going to be negative 288 2 times 6 is 12. and inside the square root symbol we have 289 minus 288 which is the square root of one and the square root of one is one so this is what we now have so we have seventeen plus one over twelve at this point when you have the plus and minus symbol you can break it up into two answers and the other answer is going to be 17 minus 1 over 12. 17 plus 1 is 18 and 17 minus 1 is 16. so now we just need to reduce those fractions so 18 is 6 times 3 twelve is six times two canceling the six we get one of our solutions as three over two for the other one sixteen we can write that as four times four twelve is four times three so canceling the four we get the other answer which is four over three and so that's it for this video now you know how to use the quadratic formula to solve a quadratic equation thanks again for watching