24x^2-54x+12=0

Solution for 24x^2-54x+12=0 equation:

24x^2-54x+12=0

a = 24; b = -54; c = +12;
Δ = b2-4ac
Δ = -542-4·24·12
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-42}{2*24}=\frac{12}{48}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+42}{2*24}=\frac{96}{48}
=2
$