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180x^2-360x-162=0
a = 180; b = -360; c = -162;
Δ = b2-4ac
Δ = -3602-4·180·(-162)
Δ = 246240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{246240}=\sqrt{1296*190}=\sqrt{1296}*\sqrt{190}=36\sqrt{190}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-36\sqrt{190}}{2*180}=\frac{360-36\sqrt{190}}{360} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+36\sqrt{190}}{2*180}=\frac{360+36\sqrt{190}}{360} $
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