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x2-23x-174=0
We add all the numbers together, and all the variables
x^2-23x-174=0
a = 1; b = -23; c = -174;
Δ = b2-4ac
Δ = -232-4·1·(-174)
Δ = 1225
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{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-35}{2*1}=\frac{-12}{2} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+35}{2*1}=\frac{58}{2} =29 $
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