5n*n=90

Solution for 5n*n=90 equation:

5n*n=90

We move all terms to the left:

5n*n-(90)=0

Wy multiply elements

5n^2-90=0

a = 5; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·5·(-90)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*5}=\frac{0-30\sqrt{2}}{10}
=-\frac{30\sqrt{2}}{10}
=-3\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*5}=\frac{0+30\sqrt{2}}{10}
=\frac{30\sqrt{2}}{10}
=3\sqrt{2}
$