66=6*(x^2)

Solution for 66=6*(x^2) equation:

66=6(x^2)

We move all terms to the left:

66-(6(x^2))=0

determiningTheFunctionDomain
-6x^2+66=0

a = -6; b = 0; c = +66;
Δ = b2-4ac
Δ = 02-4·(-6)·66
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*-6}=\frac{0-12\sqrt{11}}{-12}
=-\frac{12\sqrt{11}}{-12}
=-\frac{\sqrt{11}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*-6}=\frac{0+12\sqrt{11}}{-12}
=\frac{12\sqrt{11}}{-12}
=\frac{\sqrt{11}}{-1}
$