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9x=1/3x-2
We move all terms to the left:
9x-(1/3x-2)=0
Domain of the equation: 3x-2)!=0We get rid of parentheses
x∈R
9x-1/3x+2=0
We multiply all the terms by the denominator
9x*3x+2*3x-1=0
Wy multiply elements
27x^2+6x-1=0
a = 27; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·27·(-1)
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*27}=\frac{-18}{54} =-1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*27}=\frac{6}{54} =1/9 $
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