90=3n^2-0.75

Solution for 90=3n^2-0.75 equation:

90=3n^2-0.75

We move all terms to the left:

90-(3n^2-0.75)=0

We get rid of parentheses

-3n^2+0.75+90=0

We add all the numbers together, and all the variables

-3n^2+90.75=0

a = -3; b = 0; c = +90.75;
Δ = b2-4ac
Δ = 02-4·(-3)·90.75
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-33}{2*-3}=\frac{-33}{-6}
=5+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+33}{2*-3}=\frac{33}{-6}
=-5+1/2
$