n^2-3=19.5

Solution for n^2-3=19.5 equation:

n^2-3=19.5

We move all terms to the left:

n^2-3-(19.5)=0

We add all the numbers together, and all the variables

n^2-22.5=0

a = 1; b = 0; c = -22.5;
Δ = b2-4ac
Δ = 02-4·1·(-22.5)
Δ = 90
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:

$\sqrt{\Delta}=\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{10}}{2*1}=\frac{0-3\sqrt{10}}{2}
=-\frac{3\sqrt{10}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{10}}{2*1}=\frac{0+3\sqrt{10}}{2}
=\frac{3\sqrt{10}}{2}
$