176.76-9n-3n^2=0

Solution for 176.76-9n-3n^2=0 equation:

176.76-9n-3n^2=0

a = -3; b = -9; c = +176.76;
Δ = b2-4ac
Δ = -92-4·(-3)·176.76
Δ = 2202.12
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{2202.12}}{2*-3}=\frac{9-\sqrt{2202.12}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{2202.12}}{2*-3}=\frac{9+\sqrt{2202.12}}{-6}
$