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x=8-15/x
We move all terms to the left:
x-(8-15/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
x-(-15/x+8)=0
We get rid of parentheses
x+15/x-8=0
We multiply all the terms by the denominator
x*x-8*x+15=0
We add all the numbers together, and all the variables
-8x+x*x+15=0
Wy multiply elements
x^2-8x+15=0
a = 1; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·1·15
Δ = 4
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*1}=\frac{6}{2} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*1}=\frac{10}{2} =5 $
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