2=x(1+6x)

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

2=x(1+6x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

x(6x+1)

We multiply parentheses

6x^2+x

Back to the equation:

-(6x^2+x)


We get rid of parentheses

-6x^2-x+2=0

We add all the numbers together, and all the variables

-6x^2-1x+2=0

a = -6; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-6)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-6}=\frac{8}{-12}
=-2/3
$