3n^2-51n+156=0

Solution for 3n^2-51n+156=0 equation:

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