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2/x+9=4/3x-3
We move all terms to the left:
2/x+9-(4/3x-3)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x-3)!=0We get rid of parentheses
x∈R
2/x-4/3x+3+9=0
We calculate fractions
6x/3x^2+(-4x)/3x^2+3+9=0
We add all the numbers together, and all the variables
6x/3x^2+(-4x)/3x^2+12=0
We multiply all the terms by the denominator
6x+(-4x)+12*3x^2=0
Wy multiply elements
36x^2+6x+(-4x)=0
We get rid of parentheses
36x^2+6x-4x=0
We add all the numbers together, and all the variables
36x^2+2x=0
a = 36; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·36·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*36}=\frac{-4}{72} =-1/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*36}=\frac{0}{72} =0 $
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