(4x-7)(x+8)-(2x+3)(4x-7)=0

Solution for (4x-7)(x+8)-(2x+3)(4x-7)=0 equation:

(4x-7)(x+8)-(2x+3)(4x-7)=0

We multiply parentheses ..

(+4x^2+32x-7x-56)-(2x+3)(4x-7)=0

We get rid of parentheses

4x^2+32x-7x-(2x+3)(4x-7)-56=0

We multiply parentheses ..

4x^2-(+8x^2-14x+12x-21)+32x-7x-56=0

We add all the numbers together, and all the variables

4x^2-(+8x^2-14x+12x-21)+25x-56=0

We get rid of parentheses

4x^2-8x^2+14x-12x+25x+21-56=0

We add all the numbers together, and all the variables

-4x^2+27x-35=0

a = -4; b = 27; c = -35;
Δ = b2-4ac
Δ = 272-4·(-4)·(-35)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-13}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+13}{2*-4}=\frac{-14}{-8}
=1+3/4
$