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55x^2-113x+55=0

a = 55; b = -113; c = +55;

Δ = b^{2}-4ac

Δ = -113^{2}-4·55·55

Δ = 669

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{-(-113)-\sqrt{669}}{2*55}=\frac{113-\sqrt{669}}{110} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-113)+\sqrt{669}}{2*55}=\frac{113+\sqrt{669}}{110} $

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