(4x-20)(x-7)=0

Solution for (4x-20)(x-7)=0 equation:

(4x-20)(x-7)=0

We multiply parentheses ..

(+4x^2-28x-20x+140)=0

We get rid of parentheses

4x^2-28x-20x+140=0

We add all the numbers together, and all the variables

4x^2-48x+140=0

a = 4; b = -48; c = +140;
Δ = b2-4ac
Δ = -482-4·4·140
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8}{2*4}=\frac{40}{8}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8}{2*4}=\frac{56}{8}
=7
$