10n^2-12n-18=0

Solution for 10n^2-12n-18=0 equation:

10n^2-12n-18=0

a = 10; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·10·(-18)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{6}}{2*10}=\frac{12-12\sqrt{6}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{6}}{2*10}=\frac{12+12\sqrt{6}}{20}
$