(x+5)(3x+6)-(4x-8)(x+5)=0

Solution for (x+5)(3x+6)-(4x-8)(x+5)=0 equation:

(x+5)(3x+6)-(4x-8)(x+5)=0

We multiply parentheses ..

(+3x^2+6x+15x+30)-(4x-8)(x+5)=0

We get rid of parentheses

3x^2+6x+15x-(4x-8)(x+5)+30=0

We multiply parentheses ..

3x^2-(+4x^2+20x-8x-40)+6x+15x+30=0

We add all the numbers together, and all the variables

3x^2-(+4x^2+20x-8x-40)+21x+30=0

We get rid of parentheses

3x^2-4x^2-20x+8x+21x+40+30=0

We add all the numbers together, and all the variables

-1x^2+9x+70=0

a = -1; b = 9; c = +70;
Δ = b2-4ac
Δ = 92-4·(-1)·70
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*-1}=\frac{10}{-2}
=-5
$