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13x-2x^2=-17
We move all terms to the left:
13x-2x^2-(-17)=0
We add all the numbers together, and all the variables
-2x^2+13x+17=0
a = -2; b = 13; c = +17;
Δ = b2-4ac
Δ = 132-4·(-2)·17
Δ = 305
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{-(13)-\sqrt{305}}{2*-2}=\frac{-13-\sqrt{305}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{305}}{2*-2}=\frac{-13+\sqrt{305}}{-4} $
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