(5x+8)(3x-7)-(5-4x)(5x+8)=0

Solution for (5x+8)(3x-7)-(5-4x)(5x+8)=0 equation:

(5x+8)(3x-7)-(5-4x)(5x+8)=0

We add all the numbers together, and all the variables

(5x+8)(3x-7)-(-4x+5)(5x+8)=0

We multiply parentheses ..

(+15x^2-35x+24x-56)-(-4x+5)(5x+8)=0

We get rid of parentheses

15x^2-35x+24x-(-4x+5)(5x+8)-56=0

We multiply parentheses ..

15x^2-(-20x^2-32x+25x+40)-35x+24x-56=0

We add all the numbers together, and all the variables

15x^2-(-20x^2-32x+25x+40)-11x-56=0

We get rid of parentheses

15x^2+20x^2+32x-25x-11x-40-56=0

We add all the numbers together, and all the variables

35x^2-4x-96=0

a = 35; b = -4; c = -96;
Δ = b2-4ac
Δ = -42-4·35·(-96)
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-116}{2*35}=\frac{-112}{70}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+116}{2*35}=\frac{120}{70}
=1+5/7
$