9n^2-18n-78=0

Solution for 9n^2-18n-78=0 equation:

9n^2-18n-78=0

a = 9; b = -18; c = -78;
Δ = b2-4ac
Δ = -182-4·9·(-78)
Δ = 3132
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:

$\sqrt{\Delta}=\sqrt{3132}=\sqrt{36*87}=\sqrt{36}*\sqrt{87}=6\sqrt{87}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{87}}{2*9}=\frac{18-6\sqrt{87}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{87}}{2*9}=\frac{18+6\sqrt{87}}{18}
$