-9x^2+12x+5=0

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

-9x^2+12x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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