3(n+5)n=36

Solution for 3(n+5)n=36 equation:

3(n+5)n=36

We move all terms to the left:

3(n+5)n-(36)=0

We multiply parentheses

3n^2+15n-36=0

a = 3; b = 15; c = -36;
Δ = b2-4ac
Δ = 152-4·3·(-36)
Δ = 657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{73}}{2*3}=\frac{-15-3\sqrt{73}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{73}}{2*3}=\frac{-15+3\sqrt{73}}{6}
$