10n^2-12n-12=0

Solution for 10n^2-12n-12=0 equation:

10n^2-12n-12=0

a = 10; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·10·(-12)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{39}}{2*10}=\frac{12-4\sqrt{39}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{39}}{2*10}=\frac{12+4\sqrt{39}}{20}
$