6x^2-120x+180=0

Solution for 6x^2-120x+180=0 equation:

6x^2-120x+180=0

a = 6; b = -120; c = +180;
Δ = b2-4ac
Δ = -1202-4·6·180
Δ = 10080
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:

$\sqrt{\Delta}=\sqrt{10080}=\sqrt{144*70}=\sqrt{144}*\sqrt{70}=12\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-12\sqrt{70}}{2*6}=\frac{120-12\sqrt{70}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+12\sqrt{70}}{2*6}=\frac{120+12\sqrt{70}}{12}
$