6x2-66x+24=0

Solution for 6x2-66x+24=0 equation:

6x^2-66x+24=0

a = 6; b = -66; c = +24;
Δ = b2-4ac
Δ = -662-4·6·24
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{105}}{2*6}=\frac{66-6\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{105}}{2*6}=\frac{66+6\sqrt{105}}{12}
$