4x+8=2x(2x-8)

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

4x+8=2x(2x-8)

We move all terms to the left:

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


We calculate terms in parentheses: -(2x(2x-8)), so:

2x(2x-8)

We multiply parentheses

4x^2-16x

Back to the equation:

-(4x^2-16x)


We get rid of parentheses

-4x^2+4x+16x+8=0

We add all the numbers together, and all the variables

-4x^2+20x+8=0

a = -4; b = 20; c = +8;
Δ = b2-4ac
Δ = 202-4·(-4)·8
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{33}}{2*-4}=\frac{-20-4\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{33}}{2*-4}=\frac{-20+4\sqrt{33}}{-8}
$