9n^2-10n-20=0

Solution for 9n^2-10n-20=0 equation:

9n^2-10n-20=0

a = 9; b = -10; c = -20;
Δ = b2-4ac
Δ = -102-4·9·(-20)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{205}}{2*9}=\frac{10-2\sqrt{205}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{205}}{2*9}=\frac{10+2\sqrt{205}}{18}
$