9n^2+2n-23=0

Solution for 9n^2+2n-23=0 equation:

9n^2+2n-23=0

a = 9; b = 2; c = -23;
Δ = b2-4ac
Δ = 22-4·9·(-23)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{13}}{2*9}=\frac{-2-8\sqrt{13}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{13}}{2*9}=\frac{-2+8\sqrt{13}}{18}
$