24x-6x^2+8=0

Solution for 24x-6x^2+8=0 equation:

24x-6x^2+8=0

a = -6; b = 24; c = +8;
Δ = b2-4ac
Δ = 242-4·(-6)·8
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{3}}{2*-6}=\frac{-24-16\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{3}}{2*-6}=\frac{-24+16\sqrt{3}}{-12}
$