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X^2-18X+54=0
a = 1; b = -18; c = +54;
Δ = b2-4ac
Δ = -182-4·1·54
Δ = 108
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{3}}{2*1}=\frac{18-6\sqrt{3}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{3}}{2*1}=\frac{18+6\sqrt{3}}{2} $
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