216=6x^2-2x

Solution for 216=6x^2-2x equation:

216=6x^2-2x

We move all terms to the left:

216-(6x^2-2x)=0

We get rid of parentheses

-6x^2+2x+216=0

a = -6; b = 2; c = +216;
Δ = b2-4ac
Δ = 22-4·(-6)·216
Δ = 5188
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:

$\sqrt{\Delta}=\sqrt{5188}=\sqrt{4*1297}=\sqrt{4}*\sqrt{1297}=2\sqrt{1297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1297}}{2*-6}=\frac{-2-2\sqrt{1297}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1297}}{2*-6}=\frac{-2+2\sqrt{1297}}{-12}
$