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9x^2-107x+186=0
a = 9; b = -107; c = +186;
Δ = b2-4ac
Δ = -1072-4·9·186
Δ = 4753
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4753}=\sqrt{49*97}=\sqrt{49}*\sqrt{97}=7\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-107)-7\sqrt{97}}{2*9}=\frac{107-7\sqrt{97}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-107)+7\sqrt{97}}{2*9}=\frac{107+7\sqrt{97}}{18} $
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