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x*(x-27)=180
We move all terms to the left:
x*(x-27)-(180)=0
We multiply parentheses
x^2-27x-180=0
a = 1; b = -27; c = -180;
Δ = b2-4ac
Δ = -272-4·1·(-180)
Δ = 1449
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{161}}{2*1}=\frac{27-3\sqrt{161}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{161}}{2*1}=\frac{27+3\sqrt{161}}{2} $
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