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X^2-5X-76=0
a = 1; b = -5; c = -76;
Δ = b2-4ac
Δ = -52-4·1·(-76)
Δ = 329
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{-(-5)-\sqrt{329}}{2*1}=\frac{5-\sqrt{329}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{329}}{2*1}=\frac{5+\sqrt{329}}{2} $
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