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6x^2-17x-84=0
a = 6; b = -17; c = -84;
Δ = b2-4ac
Δ = -172-4·6·(-84)
Δ = 2305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{2305}}{2*6}=\frac{17-\sqrt{2305}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{2305}}{2*6}=\frac{17+\sqrt{2305}}{12} $
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