(x+7)(x-8)=3x

Solution for (x+7)(x-8)=3x equation:

(x+7)(x-8)=3x

We move all terms to the left:

(x+7)(x-8)-(3x)=0

We add all the numbers together, and all the variables

-3x+(x+7)(x-8)=0

We multiply parentheses ..

(+x^2-8x+7x-56)-3x=0

We get rid of parentheses

x^2-8x+7x-3x-56=0

We add all the numbers together, and all the variables

x^2-4x-56=0

a = 1; b = -4; c = -56;
Δ = b2-4ac
Δ = -42-4·1·(-56)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{15}}{2*1}=\frac{4-4\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{15}}{2*1}=\frac{4+4\sqrt{15}}{2}
$