4x(2x-5)=8x-20

Solution for 4x(2x-5)=8x-20 equation:

4x(2x-5)=8x-20

We move all terms to the left:

4x(2x-5)-(8x-20)=0

We multiply parentheses

8x^2-20x-(8x-20)=0

We get rid of parentheses

8x^2-20x-8x+20=0

We add all the numbers together, and all the variables

8x^2-28x+20=0

a = 8; b = -28; c = +20;
Δ = b2-4ac
Δ = -282-4·8·20
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12}{2*8}=\frac{16}{16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12}{2*8}=\frac{40}{16}
=2+1/2
$