x^2=2x(6x+4)

Solution for x^2=2x(6x+4) equation:

x^2=2x(6x+4)

We move all terms to the left:

x^2-(2x(6x+4))=0


We calculate terms in parentheses: -(2x(6x+4)), so:

2x(6x+4)

We multiply parentheses

12x^2+8x

Back to the equation:

-(12x^2+8x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-11x^2-8x=0

a = -11; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-11)·0
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{-(-8)-8}{2*-11}=\frac{0}{-22}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-11}=\frac{16}{-22}
=-8/11
$