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x+x^2=102
We move all terms to the left:
x+x^2-(102)=0
a = 1; b = 1; c = -102;
Δ = b2-4ac
Δ = 12-4·1·(-102)
Δ = 409
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{-(1)-\sqrt{409}}{2*1}=\frac{-1-\sqrt{409}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{409}}{2*1}=\frac{-1+\sqrt{409}}{2} $
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