3n^2+.75=90

Solution for 3n^2+.75=90 equation:

3n^2+.75=90

We move all terms to the left:

3n^2+.75-(90)=0

We add all the numbers together, and all the variables

3n^2-89.25=0

a = 3; b = 0; c = -89.25;
Δ = b2-4ac
Δ = 02-4·3·(-89.25)
Δ = 1071
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:

$\sqrt{\Delta}=\sqrt{1071}=\sqrt{9*119}=\sqrt{9}*\sqrt{119}=3\sqrt{119}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{119}}{2*3}=\frac{0-3\sqrt{119}}{6}
=-\frac{3\sqrt{119}}{6}
=-\frac{\sqrt{119}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{119}}{2*3}=\frac{0+3\sqrt{119}}{6}
=\frac{3\sqrt{119}}{6}
=\frac{\sqrt{119}}{2}
$