180=9n+4+3n^2-0.75

Solution for 180=9n+4+3n^2-0.75 equation:

180=9n+4+3n^2-0.75

We move all terms to the left:

180-(9n+4+3n^2-0.75)=0

We get rid of parentheses

-3n^2-9n-4+0.75+180=0

We add all the numbers together, and all the variables

-3n^2-9n+176.75=0

a = -3; b = -9; c = +176.75;
Δ = b2-4ac
Δ = -92-4·(-3)·176.75
Δ = 2202
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{2202}}{2*-3}=\frac{9-\sqrt{2202}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{2202}}{2*-3}=\frac{9+\sqrt{2202}}{-6}
$