3n^2+9n=176.75

Solution for 3n^2+9n=176.75 equation:

3n^2+9n=176.75

We move all terms to the left:

3n^2+9n-(176.75)=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}
$