3n^2=33n-90

Solution for 3n^2=33n-90 equation:

3n^2=33n-90

We move all terms to the left:

3n^2-(33n-90)=0

We get rid of parentheses

3n^2-33n+90=0

a = 3; b = -33; c = +90;
Δ = b2-4ac
Δ = -332-4·3·90
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*3}=\frac{30}{6}
=5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*3}=\frac{36}{6}
=6
$