10n2-30n-108=0

Solution for 10n2-30n-108=0 equation:

10n^2-30n-108=0

a = 10; b = -30; c = -108;
Δ = b2-4ac
Δ = -302-4·10·(-108)
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{145}}{2*10}=\frac{30-6\sqrt{145}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{145}}{2*10}=\frac{30+6\sqrt{145}}{20}
$