11=6x^2

Solution for 11=6x^2 equation:

11=6x^2

We move all terms to the left:

11-(6x^2)=0

a = -6; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-6)·11
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*-6}=\frac{0-2\sqrt{66}}{-12}
=-\frac{2\sqrt{66}}{-12}
=-\frac{\sqrt{66}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*-6}=\frac{0+2\sqrt{66}}{-12}
=\frac{2\sqrt{66}}{-12}
=\frac{\sqrt{66}}{-6}
$