15n^2=225

Solution for 15n^2=225 equation:

15n^2=225

We move all terms to the left:

15n^2-(225)=0

a = 15; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·15·(-225)
Δ = 13500
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:

$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{15}}{2*15}=\frac{0-30\sqrt{15}}{30}
=-\frac{30\sqrt{15}}{30}
=-\sqrt{15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{15}}{2*15}=\frac{0+30\sqrt{15}}{30}
=\frac{30\sqrt{15}}{30}
=\sqrt{15}
$