3n(2n+1)=15

Solution for 3n(2n+1)=15 equation:

3n(2n+1)=15

We move all terms to the left:

3n(2n+1)-(15)=0

We multiply parentheses

6n^2+3n-15=0

a = 6; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·6·(-15)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{41}}{2*6}=\frac{-3-3\sqrt{41}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{41}}{2*6}=\frac{-3+3\sqrt{41}}{12}
$