-12x^2-180x+464=0

Solution for -12x^2-180x+464=0 equation:

-12x^2-180x+464=0

a = -12; b = -180; c = +464;
Δ = b2-4ac
Δ = -1802-4·(-12)·464
Δ = 54672
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:

$\sqrt{\Delta}=\sqrt{54672}=\sqrt{16*3417}=\sqrt{16}*\sqrt{3417}=4\sqrt{3417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{3417}}{2*-12}=\frac{180-4\sqrt{3417}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{3417}}{2*-12}=\frac{180+4\sqrt{3417}}{-24}
$