(7-x)(x+6)-(2x+4)(x-7)=0

Solution for (7-x)(x+6)-(2x+4)(x-7)=0 equation:

(7-x)(x+6)-(2x+4)(x-7)=0

We add all the numbers together, and all the variables

(-1x+7)(x+6)-(2x+4)(x-7)=0

We multiply parentheses ..

(-1x^2-6x+7x+42)-(2x+4)(x-7)=0

We get rid of parentheses

-1x^2-6x+7x-(2x+4)(x-7)+42=0

We multiply parentheses ..

-1x^2-(+2x^2-14x+4x-28)-6x+7x+42=0

We add all the numbers together, and all the variables

-1x^2-(+2x^2-14x+4x-28)+x+42=0

We get rid of parentheses

-1x^2-2x^2+14x-4x+x+28+42=0

We add all the numbers together, and all the variables

-3x^2+11x+70=0

a = -3; b = 11; c = +70;
Δ = b2-4ac
Δ = 112-4·(-3)·70
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-31}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*-3}=\frac{20}{-6}
=-3+1/3
$