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9x^2-22x+3=0
a = 9; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·9·3
Δ = 376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{94}}{2*9}=\frac{22-2\sqrt{94}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{94}}{2*9}=\frac{22+2\sqrt{94}}{18} $
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