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x^2-23x+84=0
a = 1; b = -23; c = +84;
Δ = b2-4ac
Δ = -232-4·1·84
Δ = 193
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{-(-23)-\sqrt{193}}{2*1}=\frac{23-\sqrt{193}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{193}}{2*1}=\frac{23+\sqrt{193}}{2} $
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