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9x^2+34x+31=0
a = 9; b = 34; c = +31;
Δ = b2-4ac
Δ = 342-4·9·31
Δ = 40
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{10}}{2*9}=\frac{-34-2\sqrt{10}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{10}}{2*9}=\frac{-34+2\sqrt{10}}{18} $
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