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2x+1/x=7-3/x
We move all terms to the left:
2x+1/x-(7-3/x)=0
Domain of the equation: 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
2x+1/x-(-3/x+7)=0
We get rid of parentheses
2x+1/x+3/x-7=0
We multiply all the terms by the denominator
2x*x-7*x+1+3=0
We add all the numbers together, and all the variables
-7x+2x*x+4=0
Wy multiply elements
2x^2-7x+4=0
a = 2; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·2·4
Δ = 17
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{-(-7)-\sqrt{17}}{2*2}=\frac{7-\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{17}}{2*2}=\frac{7+\sqrt{17}}{4} $
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