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4x^2-82x+180=0
a = 4; b = -82; c = +180;
Δ = b2-4ac
Δ = -822-4·4·180
Δ = 3844
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{3844}=62$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-62}{2*4}=\frac{20}{8} =2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+62}{2*4}=\frac{144}{8} =18 $
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