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500+7x-x^2=0
We add all the numbers together, and all the variables
-1x^2+7x+500=0
a = -1; b = 7; c = +500;
Δ = b2-4ac
Δ = 72-4·(-1)·500
Δ = 2049
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{-(7)-\sqrt{2049}}{2*-1}=\frac{-7-\sqrt{2049}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{2049}}{2*-1}=\frac{-7+\sqrt{2049}}{-2} $
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