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18x^2-86x+72=0
a = 18; b = -86; c = +72;
Δ = b2-4ac
Δ = -862-4·18·72
Δ = 2212
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2212}=\sqrt{4*553}=\sqrt{4}*\sqrt{553}=2\sqrt{553}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{553}}{2*18}=\frac{86-2\sqrt{553}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{553}}{2*18}=\frac{86+2\sqrt{553}}{36} $
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