1) To write the equation in the standard form
![ax^{2} + bx + c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%20%3D%200)
you need to take everything to the left side and multiply everything, if necessary, to get all whole integers:
![x^{2} + 8x = 10 \\ x^{2} + 8x - 10 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%208x%20%3D%2010%20%5C%5C%20x%5E%7B2%7D%20%2B%208x%20-%2010%20%3D%200)
This will be your standard form of the equation.
2) To find a, b, c you just need to remember that:
- a is a coefficient in front of x^2
- b is a coefficient in front of x
- c is a constant with no x.
So, in your rewritten equation
![x^{2} + 8x - 10 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%208x%20-%2010%20%3D%200)
you have a = 1, b = 8, and c = -10
3) To solve the equation using quadratic formula, you need:
- find the Discriminant D, which is
![D = b^{2} - 4ac](https://tex.z-dn.net/?f=D%20%3D%20b%5E%7B2%7D%20-%204ac)
- if D < 0 there is no solution
- if D = 0 there is one solution
![x = - \frac{b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20-%20%5Cfrac%7Bb%7D%7B2a%7D%20)
- if D > 0 there are two solutions which are
![x_{1} = \frac{-b + \sqrt{D} }{2a} \\ x_{2} = \frac{-b - \sqrt{D} }{2a}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%20%5Cfrac%7B-b%20%2B%20%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%20%5C%5C%20x_%7B2%7D%20%3D%20%20%5Cfrac%7B-b%20-%20%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%20)
4) Let's solve the equation:
-
![D = b^{2} - 4ac = (8)(8) - (4)(1)(-10) = 64 - (-40) = 104](https://tex.z-dn.net/?f=D%20%3D%20b%5E%7B2%7D%20-%204ac%20%3D%20%288%29%288%29%20-%20%284%29%281%29%28-10%29%20%3D%2064%20-%20%28-40%29%20%3D%20104)
- 104 > 0 => there are 2 solutions
-
![x_{1} = \frac{-b + \sqrt{D} }{2a} = \frac{-(8) + \sqrt{104} }{(2)(1)} = \frac{-8 + \sqrt{26 * 4} }{2} = \frac{-8 + 2 \sqrt{26} }{2} = -4 + \sqrt{26} \\ x_{2} = \frac{-b - \sqrt{D} }{2a} = \frac{-(8) - \sqrt{104} }{(2)(1)} = \frac{-8 - \sqrt{26 * 4} }{2} = \frac{-8 - 2 \sqrt{26} }{2} = -4 - \sqrt{26}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%20%5Cfrac%7B-b%20%2B%20%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%20%3D%20%20%5Cfrac%7B-%288%29%20%2B%20%20%5Csqrt%7B104%7D%20%7D%7B%282%29%281%29%7D%20%3D%20%20%5Cfrac%7B-8%20%2B%20%20%5Csqrt%7B26%20%2A%204%7D%20%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B-8%20%2B%202%20%5Csqrt%7B26%7D%20%7D%7B2%7D%20%20%3D%20-4%20%2B%20%20%5Csqrt%7B26%7D%20%20%5C%5C%20x_%7B2%7D%20%3D%20%20%5Cfrac%7B-b%20-%20%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%20%3D%20%20%5Cfrac%7B-%288%29%20-%20%20%5Csqrt%7B104%7D%20%7D%7B%282%29%281%29%7D%20%3D%20%20%5Cfrac%7B-8%20-%20%20%5Csqrt%7B26%20%2A%204%7D%20%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B-8%20-%202%20%5Csqrt%7B26%7D%20%7D%7B2%7D%20%20%3D%20-4%20-%20%20%5Csqrt%7B26%7D%20)
5) So, this is your solution. Good luck!