6n^2+6n-14=0

Solution for 6n^2+6n-14=0 equation:

6n^2+6n-14=0

a = 6; b = 6; c = -14;
Δ = b2-4ac
Δ = 62-4·6·(-14)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{93}}{2*6}=\frac{-6-2\sqrt{93}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{93}}{2*6}=\frac{-6+2\sqrt{93}}{12}
$