6x-6x^2=1

Solution for 6x-6x^2=1 equation:

6x-6x^2=1

We move all terms to the left:

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

a = -6; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-6)·(-1)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*-6}=\frac{-6-2\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*-6}=\frac{-6+2\sqrt{3}}{-12}
$