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9x^2-33x+17=0
a = 9; b = -33; c = +17;
Δ = b2-4ac
Δ = -332-4·9·17
Δ = 477
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{53}}{2*9}=\frac{33-3\sqrt{53}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{53}}{2*9}=\frac{33+3\sqrt{53}}{18} $
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