-6x^2+6(36-x^2)=0

Solution for -6x^2+6(36-x^2)=0 equation:

-6x^2+6(36-x^2)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-12x^2+216=0

a = -12; b = 0; c = +216;
Δ = b2-4ac
Δ = 02-4·(-12)·216
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{2}}{2*-12}=\frac{0-72\sqrt{2}}{-24}
=-\frac{72\sqrt{2}}{-24}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{2}}{2*-12}=\frac{0+72\sqrt{2}}{-24}
=\frac{72\sqrt{2}}{-24}
=\frac{3\sqrt{2}}{-1}
$