117-88x-12x^2=0

Solution for 117-88x-12x^2=0 equation:

117-88x-12x^2=0

a = -12; b = -88; c = +117;
Δ = b2-4ac
Δ = -882-4·(-12)·117
Δ = 13360
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:

$\sqrt{\Delta}=\sqrt{13360}=\sqrt{16*835}=\sqrt{16}*\sqrt{835}=4\sqrt{835}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{835}}{2*-12}=\frac{88-4\sqrt{835}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{835}}{2*-12}=\frac{88+4\sqrt{835}}{-24}
$