2x-2=6x(x+3)

Solution for 2x-2=6x(x+3) equation:

2x-2=6x(x+3)

We move all terms to the left:

2x-2-(6x(x+3))=0


We calculate terms in parentheses: -(6x(x+3)), so:

6x(x+3)

We multiply parentheses

6x^2+18x

Back to the equation:

-(6x^2+18x)


We get rid of parentheses

-6x^2+2x-18x-2=0

We add all the numbers together, and all the variables

-6x^2-16x-2=0

a = -6; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·(-6)·(-2)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{13}}{2*-6}=\frac{16-4\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{13}}{2*-6}=\frac{16+4\sqrt{13}}{-12}
$