21n^2-12n-12=0

Solution for 21n^2-12n-12=0 equation:

21n^2-12n-12=0

a = 21; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·21·(-12)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24\sqrt{2}}{2*21}=\frac{12-24\sqrt{2}}{42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24\sqrt{2}}{2*21}=\frac{12+24\sqrt{2}}{42}
$