24x^2-320x+768=0

Solution for 24x^2-320x+768=0 equation:

24x^2-320x+768=0

a = 24; b = -320; c = +768;
Δ = b2-4ac
Δ = -3202-4·24·768
Δ = 28672
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:

$\sqrt{\Delta}=\sqrt{28672}=\sqrt{4096*7}=\sqrt{4096}*\sqrt{7}=64\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-64\sqrt{7}}{2*24}=\frac{320-64\sqrt{7}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+64\sqrt{7}}{2*24}=\frac{320+64\sqrt{7}}{48}
$