(4x-7)(x-8)=0

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

(4x-7)(x-8)=0

We multiply parentheses ..

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

We get rid of parentheses

4x^2-32x-7x+56=0

We add all the numbers together, and all the variables

4x^2-39x+56=0

a = 4; b = -39; c = +56;
Δ = b2-4ac
Δ = -392-4·4·56
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-25}{2*4}=\frac{14}{8}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+25}{2*4}=\frac{64}{8}
=8
$