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x^2-18x=-18
We move all terms to the left:
x^2-18x-(-18)=0
We add all the numbers together, and all the variables
x^2-18x+18=0
a = 1; b = -18; c = +18;
Δ = b2-4ac
Δ = -182-4·1·18
Δ = 252
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{7}}{2*1}=\frac{18-6\sqrt{7}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{7}}{2*1}=\frac{18+6\sqrt{7}}{2} $
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