9n^2-8n-10=0

Solution for 9n^2-8n-10=0 equation:

9n^2-8n-10=0

a = 9; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·9·(-10)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{106}}{2*9}=\frac{8-2\sqrt{106}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{106}}{2*9}=\frac{8+2\sqrt{106}}{18}
$