6n^2+90n-336=0

Solution for 6n^2+90n-336=0 equation:

6n^2+90n-336=0

a = 6; b = 90; c = -336;
Δ = b2-4ac
Δ = 902-4·6·(-336)
Δ = 16164
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:

$\sqrt{\Delta}=\sqrt{16164}=\sqrt{36*449}=\sqrt{36}*\sqrt{449}=6\sqrt{449}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{449}}{2*6}=\frac{-90-6\sqrt{449}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{449}}{2*6}=\frac{-90+6\sqrt{449}}{12}
$