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18x^2-60x+47=0
a = 18; b = -60; c = +47;
Δ = b2-4ac
Δ = -602-4·18·47
Δ = 216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{6}}{2*18}=\frac{60-6\sqrt{6}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{6}}{2*18}=\frac{60+6\sqrt{6}}{36} $
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