51n-3n^2=156

Solution for 51n-3n^2=156 equation:

51n-3n^2=156

We move all terms to the left:

51n-3n^2-(156)=0

a = -3; b = 51; c = -156;
Δ = b2-4ac
Δ = 512-4·(-3)·(-156)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-27}{2*-3}=\frac{-78}{-6}
=+13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+27}{2*-3}=\frac{-24}{-6}
=+4
$