-6a^2+81=0

Solution for -6a^2+81=0 equation:

-6a^2+81=0

a = -6; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-6)·81
Δ = 1944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{6}}{2*-6}=\frac{0-18\sqrt{6}}{-12}
=-\frac{18\sqrt{6}}{-12}
=-\frac{3\sqrt{6}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{6}}{2*-6}=\frac{0+18\sqrt{6}}{-12}
=\frac{18\sqrt{6}}{-12}
=\frac{3\sqrt{6}}{-2}
$