10n^2-10n-12=0

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

10n^2-10n-12=0

a = 10; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·10·(-12)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{145}}{2*10}=\frac{10-2\sqrt{145}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{145}}{2*10}=\frac{10+2\sqrt{145}}{20}
$