n(3n+17)=252

Solution for n(3n+17)=252 equation:

n(3n+17)=252

We move all terms to the left:

n(3n+17)-(252)=0

We multiply parentheses

3n^2+17n-252=0

a = 3; b = 17; c = -252;
Δ = b2-4ac
Δ = 172-4·3·(-252)
Δ = 3313
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{-(17)-\sqrt{3313}}{2*3}=\frac{-17-\sqrt{3313}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{3313}}{2*3}=\frac{-17+\sqrt{3313}}{6}
$