2x(2x-6)=(x+8)

Solution for 2x(2x-6)=(x+8) equation:

2x(2x-6)=(x+8)

We move all terms to the left:

2x(2x-6)-((x+8))=0

We multiply parentheses

4x^2-12x-((x+8))=0


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

(x+8)

We get rid of parentheses

x+8

Back to the equation:

-(x+8)


We get rid of parentheses

4x^2-12x-x-8=0

We add all the numbers together, and all the variables

4x^2-13x-8=0

a = 4; b = -13; c = -8;
Δ = b2-4ac
Δ = -132-4·4·(-8)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{33}}{2*4}=\frac{13-3\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{33}}{2*4}=\frac{13+3\sqrt{33}}{8}
$