10-2n^2=-90

Solution for 10-2n^2=-90 equation:

10-2n^2=-90

We move all terms to the left:

10-2n^2-(-90)=0

We add all the numbers together, and all the variables

-2n^2+100=0

a = -2; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-2)·100
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*-2}=\frac{0-20\sqrt{2}}{-4}
=-\frac{20\sqrt{2}}{-4}
=-\frac{5\sqrt{2}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*-2}=\frac{0+20\sqrt{2}}{-4}
=\frac{20\sqrt{2}}{-4}
=\frac{5\sqrt{2}}{-1}
$