6x^2-84x+180=0

Solution for 6x^2-84x+180=0 equation:

6x^2-84x+180=0

a = 6; b = -84; c = +180;
Δ = b2-4ac
Δ = -842-4·6·180
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{19}}{2*6}=\frac{84-12\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{19}}{2*6}=\frac{84+12\sqrt{19}}{12}
$