6x2-54x+24=0

Solution for 6x2-54x+24=0 equation:

6x^2-54x+24=0

a = 6; b = -54; c = +24;
Δ = b2-4ac
Δ = -542-4·6·24
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{65}}{2*6}=\frac{54-6\sqrt{65}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{65}}{2*6}=\frac{54+6\sqrt{65}}{12}
$