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x^2-27x+121=0
a = 1; b = -27; c = +121;
Δ = b2-4ac
Δ = -272-4·1·121
Δ = 245
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-7\sqrt{5}}{2*1}=\frac{27-7\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+7\sqrt{5}}{2*1}=\frac{27+7\sqrt{5}}{2} $
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