3x2-64x+24=0

Solution for 3x2-64x+24=0 equation:

3x^2-64x+24=0

a = 3; b = -64; c = +24;
Δ = b2-4ac
Δ = -642-4·3·24
Δ = 3808
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:

$\sqrt{\Delta}=\sqrt{3808}=\sqrt{16*238}=\sqrt{16}*\sqrt{238}=4\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{238}}{2*3}=\frac{64-4\sqrt{238}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{238}}{2*3}=\frac{64+4\sqrt{238}}{6}
$