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x-4/5x+1=x+4/x
We move all terms to the left:
x-4/5x+1-(x+4/x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
x-4/5x-(+x+4/x)+1=0
We get rid of parentheses
x-4/5x-x-4/x+1=0
We calculate fractions
x-x+(-4x)/5x^2+(-20x)/5x^2+1=0
We add all the numbers together, and all the variables
(-4x)/5x^2+(-20x)/5x^2+1=0
We multiply all the terms by the denominator
(-4x)+(-20x)+1*5x^2=0
Wy multiply elements
5x^2+(-4x)+(-20x)=0
We get rid of parentheses
5x^2-4x-20x=0
We add all the numbers together, and all the variables
5x^2-24x=0
a = 5; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·5·0
Δ = 576
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{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*5}=\frac{0}{10} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*5}=\frac{48}{10} =4+4/5 $
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