6x^2-54x+80=0

Solution for 6x^2-54x+80=0 equation:

6x^2-54x+80=0

a = 6; b = -54; c = +80;
Δ = b2-4ac
Δ = -542-4·6·80
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{249}}{2*6}=\frac{54-2\sqrt{249}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{249}}{2*6}=\frac{54+2\sqrt{249}}{12}
$