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1/x+1/3x=8/9
We move all terms to the left:
1/x+1/3x-(8/9)=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!=0/3
x!=0
x∈R
1/x+1/3x-(+8/9)=0
We get rid of parentheses
1/x+1/3x-8/9=0
We calculate fractions
(-72x^2)/243x^2+243x/243x^2+81x/243x^2=0
We multiply all the terms by the denominator
(-72x^2)+243x+81x=0
We add all the numbers together, and all the variables
(-72x^2)+324x=0
We get rid of parentheses
-72x^2+324x=0
a = -72; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-72)·0
Δ = 104976
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{104976}=324$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-324}{2*-72}=\frac{-648}{-144} =4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-72}=\frac{0}{-144} =0 $
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