2=2x(6x+1)

Solution for 2=2x(6x+1) equation:

2=2x(6x+1)

We move all terms to the left:

2-(2x(6x+1))=0


We calculate terms in parentheses: -(2x(6x+1)), so:

2x(6x+1)

We multiply parentheses

12x^2+2x

Back to the equation:

-(12x^2+2x)


We get rid of parentheses

-12x^2-2x+2=0

a = -12; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-12)·2
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-12}=\frac{-8}{-24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-12}=\frac{12}{-24}
=-1/2
$