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13.9x+5x^2=500
We move all terms to the left:
13.9x+5x^2-(500)=0
a = 5; b = 13.9; c = -500;
Δ = b2-4ac
Δ = 13.92-4·5·(-500)
Δ = 10193.21
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{-(13.9)-\sqrt{10193.21}}{2*5}=\frac{-13.9-\sqrt{10193.21}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13.9)+\sqrt{10193.21}}{2*5}=\frac{-13.9+\sqrt{10193.21}}{10} $
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