12x^2-48x+24=0

Solution for 12x^2-48x+24=0 equation:

12x^2-48x+24=0

a = 12; b = -48; c = +24;
Δ = b2-4ac
Δ = -482-4·12·24
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{2}}{2*12}=\frac{48-24\sqrt{2}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{2}}{2*12}=\frac{48+24\sqrt{2}}{24}
$