36n^2-18n-45=0

Solution for 36n^2-18n-45=0 equation:

36n^2-18n-45=0

a = 36; b = -18; c = -45;
Δ = b2-4ac
Δ = -182-4·36·(-45)
Δ = 6804
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:

$\sqrt{\Delta}=\sqrt{6804}=\sqrt{324*21}=\sqrt{324}*\sqrt{21}=18\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{21}}{2*36}=\frac{18-18\sqrt{21}}{72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{21}}{2*36}=\frac{18+18\sqrt{21}}{72}
$