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4/9x+5/3=2+2/3x
We move all terms to the left:
4/9x+5/3-(2+2/3x)=0
Domain of the equation: 9x!=0
x!=0/9
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
4/9x-(2/3x+2)+5/3=0
We get rid of parentheses
4/9x-2/3x-2+5/3=0
We calculate fractions
108x/243x^2+(-18x)/243x^2+45x/243x^2-2=0
We multiply all the terms by the denominator
108x+(-18x)+45x-2*243x^2=0
We add all the numbers together, and all the variables
153x+(-18x)-2*243x^2=0
Wy multiply elements
-486x^2+153x+(-18x)=0
We get rid of parentheses
-486x^2+153x-18x=0
We add all the numbers together, and all the variables
-486x^2+135x=0
a = -486; b = 135; c = 0;
Δ = b2-4ac
Δ = 1352-4·(-486)·0
Δ = 18225
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{18225}=135$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-135}{2*-486}=\frac{-270}{-972} =5/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+135}{2*-486}=\frac{0}{-972} =0 $
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