9n^2-9n-510=0

Solution for 9n^2-9n-510=0 equation:

9n^2-9n-510=0

a = 9; b = -9; c = -510;
Δ = b2-4ac
Δ = -92-4·9·(-510)
Δ = 18441
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:

$\sqrt{\Delta}=\sqrt{18441}=\sqrt{9*2049}=\sqrt{9}*\sqrt{2049}=3\sqrt{2049}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{2049}}{2*9}=\frac{9-3\sqrt{2049}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{2049}}{2*9}=\frac{9+3\sqrt{2049}}{18}
$