3n^2+9n+4.75=180

Solution for 3n^2+9n+4.75=180 equation:

3n^2+9n+4.75=180

We move all terms to the left:

3n^2+9n+4.75-(180)=0

We add all the numbers together, and all the variables

3n^2+9n-175.25=0

a = 3; b = 9; c = -175.25;
Δ = b2-4ac
Δ = 92-4·3·(-175.25)
Δ = 2184
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:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-2\sqrt{546}}{2*3}=\frac{-9-2\sqrt{546}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+2\sqrt{546}}{2*3}=\frac{-9+2\sqrt{546}}{6}
$