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2x^2-33x-109=0
a = 2; b = -33; c = -109;
Δ = b2-4ac
Δ = -332-4·2·(-109)
Δ = 1961
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{-(-33)-\sqrt{1961}}{2*2}=\frac{33-\sqrt{1961}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1961}}{2*2}=\frac{33+\sqrt{1961}}{4} $
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