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11x^2-3x-1=0
a = 11; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·11·(-1)
Δ = 53
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{-(-3)-\sqrt{53}}{2*11}=\frac{3-\sqrt{53}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{53}}{2*11}=\frac{3+\sqrt{53}}{22} $
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