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177.5-8.33x=x^2
We move all terms to the left:
177.5-8.33x-(x^2)=0
determiningTheFunctionDomain -x^2-8.33x+177.5=0
We add all the numbers together, and all the variables
-1x^2-8.33x+177.5=0
a = -1; b = -8.33; c = +177.5;
Δ = b2-4ac
Δ = -8.332-4·(-1)·177.5
Δ = 779.3889
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{-(-8.33)-\sqrt{779.3889}}{2*-1}=\frac{8.33-\sqrt{779.3889}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.33)+\sqrt{779.3889}}{2*-1}=\frac{8.33+\sqrt{779.3889}}{-2} $
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