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4x^2-33x+7=0
a = 4; b = -33; c = +7;
Δ = b2-4ac
Δ = -332-4·4·7
Δ = 977
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{977}}{2*4}=\frac{33-\sqrt{977}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{977}}{2*4}=\frac{33+\sqrt{977}}{8} $
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