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17x^2+12x-5=0
a = 17; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·17·(-5)
Δ = 484
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-22}{2*17}=\frac{-34}{34} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+22}{2*17}=\frac{10}{34} =5/17 $
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