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5x-1=8/x
We move all terms to the left:
5x-1-(8/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5x-(+8/x)-1=0
We get rid of parentheses
5x-8/x-1=0
We multiply all the terms by the denominator
5x*x-1*x-8=0
We add all the numbers together, and all the variables
-1x+5x*x-8=0
Wy multiply elements
5x^2-1x-8=0
a = 5; b = -1; c = -8;
Δ = b2-4ac
Δ = -12-4·5·(-8)
Δ = 161
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{-(-1)-\sqrt{161}}{2*5}=\frac{1-\sqrt{161}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161}}{2*5}=\frac{1+\sqrt{161}}{10} $
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