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x^2+34x-111=0
a = 1; b = 34; c = -111;
Δ = b2-4ac
Δ = 342-4·1·(-111)
Δ = 1600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1600}=40$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-40}{2*1}=\frac{-74}{2} =-37 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+40}{2*1}=\frac{6}{2} =3 $
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