9n2-2n-6=0

Solution for 9n2-2n-6=0 equation:

9n^2-2n-6=0

a = 9; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·9·(-6)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{55}}{2*9}=\frac{2-2\sqrt{55}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{55}}{2*9}=\frac{2+2\sqrt{55}}{18}
$