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17x-x^2=18
We move all terms to the left:
17x-x^2-(18)=0
We add all the numbers together, and all the variables
-1x^2+17x-18=0
a = -1; b = 17; c = -18;
Δ = b2-4ac
Δ = 172-4·(-1)·(-18)
Δ = 217
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{-(17)-\sqrt{217}}{2*-1}=\frac{-17-\sqrt{217}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{217}}{2*-1}=\frac{-17+\sqrt{217}}{-2} $
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