(x+2)(x-7)=8x

Solution for (x+2)(x-7)=8x equation:

(x+2)(x-7)=8x

We move all terms to the left:

(x+2)(x-7)-(8x)=0

We add all the numbers together, and all the variables

-8x+(x+2)(x-7)=0

We multiply parentheses ..

(+x^2-7x+2x-14)-8x=0

We get rid of parentheses

x^2-7x+2x-8x-14=0

We add all the numbers together, and all the variables

x^2-13x-14=0

a = 1; b = -13; c = -14;
Δ = b2-4ac
Δ = -132-4·1·(-14)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*1}=\frac{28}{2}
=14
$