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9x^2-2x-23=0
a = 9; b = -2; c = -23;
Δ = b2-4ac
Δ = -22-4·9·(-23)
Δ = 832
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{13}}{2*9}=\frac{2-8\sqrt{13}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{13}}{2*9}=\frac{2+8\sqrt{13}}{18} $
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