-24x^2-56x+32=0

Solution for -24x^2-56x+32=0 equation:

-24x^2-56x+32=0

a = -24; b = -56; c = +32;
Δ = b2-4ac
Δ = -562-4·(-24)·32
Δ = 6208
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:

$\sqrt{\Delta}=\sqrt{6208}=\sqrt{64*97}=\sqrt{64}*\sqrt{97}=8\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{97}}{2*-24}=\frac{56-8\sqrt{97}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{97}}{2*-24}=\frac{56+8\sqrt{97}}{-48}
$