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

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

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

We multiply parentheses ..

(+5X^2+4X-40X-32)-(X+8)(3X+6)=0

We get rid of parentheses

5X^2+4X-40X-(X+8)(3X+6)-32=0

We multiply parentheses ..

5X^2-(+3X^2+6X+24X+48)+4X-40X-32=0

We add all the numbers together, and all the variables

5X^2-(+3X^2+6X+24X+48)-36X-32=0

We get rid of parentheses

5X^2-3X^2-6X-24X-36X-48-32=0

We add all the numbers together, and all the variables

2X^2-66X-80=0

a = 2; b = -66; c = -80;
Δ = b2-4ac
Δ = -662-4·2·(-80)
Δ = 4996
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:

$\sqrt{\Delta}=\sqrt{4996}=\sqrt{4*1249}=\sqrt{4}*\sqrt{1249}=2\sqrt{1249}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1249}}{2*2}=\frac{66-2\sqrt{1249}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1249}}{2*2}=\frac{66+2\sqrt{1249}}{4}
$