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18x^2-66x=60
We move all terms to the left:
18x^2-66x-(60)=0
a = 18; b = -66; c = -60;
Δ = b2-4ac
Δ = -662-4·18·(-60)
Δ = 8676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8676}=\sqrt{36*241}=\sqrt{36}*\sqrt{241}=6\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{241}}{2*18}=\frac{66-6\sqrt{241}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{241}}{2*18}=\frac{66+6\sqrt{241}}{36} $
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