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17x^2-12x-9=0
a = 17; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·17·(-9)
Δ = 756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{21}}{2*17}=\frac{12-6\sqrt{21}}{34} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{21}}{2*17}=\frac{12+6\sqrt{21}}{34} $
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