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8x+x^2=100-x
We move all terms to the left:
8x+x^2-(100-x)=0
We add all the numbers together, and all the variables
x^2+8x-(-1x+100)=0
We get rid of parentheses
x^2+8x+1x-100=0
We add all the numbers together, and all the variables
x^2+9x-100=0
a = 1; b = 9; c = -100;
Δ = b2-4ac
Δ = 92-4·1·(-100)
Δ = 481
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{-(9)-\sqrt{481}}{2*1}=\frac{-9-\sqrt{481}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{481}}{2*1}=\frac{-9+\sqrt{481}}{2} $
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