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9x^2-34x-229=0
a = 9; b = -34; c = -229;
Δ = b2-4ac
Δ = -342-4·9·(-229)
Δ = 9400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9400}=\sqrt{100*94}=\sqrt{100}*\sqrt{94}=10\sqrt{94}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-10\sqrt{94}}{2*9}=\frac{34-10\sqrt{94}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+10\sqrt{94}}{2*9}=\frac{34+10\sqrt{94}}{18} $
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