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x^2-27x+130=0
a = 1; b = -27; c = +130;
Δ = b2-4ac
Δ = -272-4·1·130
Δ = 209
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{-(-27)-\sqrt{209}}{2*1}=\frac{27-\sqrt{209}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{209}}{2*1}=\frac{27+\sqrt{209}}{2} $
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