9-6a^2=-107

Solution for 9-6a^2=-107 equation:

9-6a^2=-107

We move all terms to the left:

9-6a^2-(-107)=0

We add all the numbers together, and all the variables

-6a^2+116=0

a = -6; b = 0; c = +116;
Δ = b2-4ac
Δ = 02-4·(-6)·116
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{174}}{2*-6}=\frac{0-4\sqrt{174}}{-12}
=-\frac{4\sqrt{174}}{-12}
=-\frac{\sqrt{174}}{-3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{174}}{2*-6}=\frac{0+4\sqrt{174}}{-12}
=\frac{4\sqrt{174}}{-12}
=\frac{\sqrt{174}}{-3}
$