-6x^2+44x-24=0

Solution for -6x^2+44x-24=0 equation:

-6x^2+44x-24=0

a = -6; b = 44; c = -24;
Δ = b2-4ac
Δ = 442-4·(-6)·(-24)
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{85}}{2*-6}=\frac{-44-4\sqrt{85}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{85}}{2*-6}=\frac{-44+4\sqrt{85}}{-12}
$