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36x^2-180x+6=0
a = 36; b = -180; c = +6;
Δ = b2-4ac
Δ = -1802-4·36·6
Δ = 31536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31536}=\sqrt{144*219}=\sqrt{144}*\sqrt{219}=12\sqrt{219}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{219}}{2*36}=\frac{180-12\sqrt{219}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{219}}{2*36}=\frac{180+12\sqrt{219}}{72} $
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