9-10n^2=-126

Solution for 9-10n^2=-126 equation:

9-10n^2=-126

We move all terms to the left:

9-10n^2-(-126)=0

We add all the numbers together, and all the variables

-10n^2+135=0

a = -10; b = 0; c = +135;
Δ = b2-4ac
Δ = 02-4·(-10)·135
Δ = 5400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{6}}{2*-10}=\frac{0-30\sqrt{6}}{-20}
=-\frac{30\sqrt{6}}{-20}
=-\frac{3\sqrt{6}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{6}}{2*-10}=\frac{0+30\sqrt{6}}{-20}
=\frac{30\sqrt{6}}{-20}
=\frac{3\sqrt{6}}{-2}
$