-9a^2=-414

Solution for -9a^2=-414 equation:

-9a^2=-414

We move all terms to the left:

-9a^2-(-414)=0

We add all the numbers together, and all the variables

-9a^2+414=0

a = -9; b = 0; c = +414;
Δ = b2-4ac
Δ = 02-4·(-9)·414
Δ = 14904
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:

$\sqrt{\Delta}=\sqrt{14904}=\sqrt{324*46}=\sqrt{324}*\sqrt{46}=18\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{46}}{2*-9}=\frac{0-18\sqrt{46}}{-18}
=-\frac{18\sqrt{46}}{-18}
=-\frac{\sqrt{46}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{46}}{2*-9}=\frac{0+18\sqrt{46}}{-18}
=\frac{18\sqrt{46}}{-18}
=\frac{\sqrt{46}}{-1}
$