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4x^2-11x-33=0
a = 4; b = -11; c = -33;
Δ = b2-4ac
Δ = -112-4·4·(-33)
Δ = 649
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{649}}{2*4}=\frac{11-\sqrt{649}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{649}}{2*4}=\frac{11+\sqrt{649}}{8} $
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