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

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

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

a = -9; b = 9; c = +12;
Δ = b2-4ac
Δ = 92-4·(-9)·12
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{57}}{2*-9}=\frac{-9-3\sqrt{57}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{57}}{2*-9}=\frac{-9+3\sqrt{57}}{-18}
$