9n^2+12n-5=0

Solution for 9n^2+12n-5=0 equation:

9n^2+12n-5=0

a = 9; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·9·(-5)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*9}=\frac{-30}{18}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*9}=\frac{6}{18}
=1/3
$