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2x^2-11x-42=0
a = 2; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·2·(-42)
Δ = 457
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{-(-11)-\sqrt{457}}{2*2}=\frac{11-\sqrt{457}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{457}}{2*2}=\frac{11+\sqrt{457}}{4} $
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