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x^2-23x-122=0
a = 1; b = -23; c = -122;
Δ = b2-4ac
Δ = -232-4·1·(-122)
Δ = 1017
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3\sqrt{113}}{2*1}=\frac{23-3\sqrt{113}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3\sqrt{113}}{2*1}=\frac{23+3\sqrt{113}}{2} $
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