6n^2+3n-21=0

Solution for 6n^2+3n-21=0 equation:

6n^2+3n-21=0

a = 6; b = 3; c = -21;
Δ = b2-4ac
Δ = 32-4·6·(-21)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{57}}{2*6}=\frac{-3-3\sqrt{57}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{57}}{2*6}=\frac{-3+3\sqrt{57}}{12}
$