6n^2+8n-12=0

Solution for 6n^2+8n-12=0 equation:

6n^2+8n-12=0

a = 6; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·6·(-12)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*6}=\frac{-8-4\sqrt{22}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*6}=\frac{-8+4\sqrt{22}}{12}
$