-24x^2-16x+480=0

Solution for -24x^2-16x+480=0 equation:

-24x^2-16x+480=0

a = -24; b = -16; c = +480;
Δ = b2-4ac
Δ = -162-4·(-24)·480
Δ = 46336
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:

$\sqrt{\Delta}=\sqrt{46336}=\sqrt{256*181}=\sqrt{256}*\sqrt{181}=16\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{181}}{2*-24}=\frac{16-16\sqrt{181}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{181}}{2*-24}=\frac{16+16\sqrt{181}}{-48}
$