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18X^2-2X-86=0
a = 18; b = -2; c = -86;
Δ = b2-4ac
Δ = -22-4·18·(-86)
Δ = 6196
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6196}=\sqrt{4*1549}=\sqrt{4}*\sqrt{1549}=2\sqrt{1549}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{1549}}{2*18}=\frac{2-2\sqrt{1549}}{36} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{1549}}{2*18}=\frac{2+2\sqrt{1549}}{36} $
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