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

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

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

We multiply parentheses ..

(+4x^2-28x-8x+56)=0

We get rid of parentheses

4x^2-28x-8x+56=0

We add all the numbers together, and all the variables

4x^2-36x+56=0

a = 4; b = -36; c = +56;
Δ = b2-4ac
Δ = -362-4·4·56
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20}{2*4}=\frac{56}{8}
=7
$