3n^2+2n=15

Solution for 3n^2+2n=15 equation:

3n^2+2n=15

We move all terms to the left:

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

a = 3; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·3·(-15)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{46}}{2*3}=\frac{-2-2\sqrt{46}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{46}}{2*3}=\frac{-2+2\sqrt{46}}{6}
$