9x^2-12x-117=0

Solution for 9x^2-12x-117=0 equation:

9x^2-12x-117=0

a = 9; b = -12; c = -117;
Δ = b2-4ac
Δ = -122-4·9·(-117)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-66}{2*9}=\frac{-54}{18}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+66}{2*9}=\frac{78}{18}
=4+1/3
$