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30/x=x+1
We move all terms to the left:
30/x-(x+1)=0
Domain of the equation: x!=0We get rid of parentheses
x∈R
30/x-x-1=0
We multiply all the terms by the denominator
-x*x-1*x+30=0
We add all the numbers together, and all the variables
-1x-x*x+30=0
Wy multiply elements
-1x^2-1x+30=0
a = -1; b = -1; c = +30;
Δ = b2-4ac
Δ = -12-4·(-1)·30
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-1}=\frac{-10}{-2} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-1}=\frac{12}{-2} =-6 $
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