6n^2+2n-15=0

Solution for 6n^2+2n-15=0 equation:

6n^2+2n-15=0

a = 6; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·6·(-15)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*6}=\frac{-2-2\sqrt{91}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*6}=\frac{-2+2\sqrt{91}}{12}
$