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4/x+2=11/3x
We move all terms to the left:
4/x+2-(11/3x)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
4/x-(+11/3x)+2=0
We get rid of parentheses
4/x-11/3x+2=0
We calculate fractions
12x/3x^2+(-11x)/3x^2+2=0
We multiply all the terms by the denominator
12x+(-11x)+2*3x^2=0
Wy multiply elements
6x^2+12x+(-11x)=0
We get rid of parentheses
6x^2+12x-11x=0
We add all the numbers together, and all the variables
6x^2+x=0
a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*6}=\frac{-2}{12} =-1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12} =0 $
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