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4/9x+2=2/3x-8
We move all terms to the left:
4/9x+2-(2/3x-8)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 3x-8)!=0We get rid of parentheses
x∈R
4/9x-2/3x+8+2=0
We calculate fractions
12x/27x^2+(-18x)/27x^2+8+2=0
We add all the numbers together, and all the variables
12x/27x^2+(-18x)/27x^2+10=0
We multiply all the terms by the denominator
12x+(-18x)+10*27x^2=0
Wy multiply elements
270x^2+12x+(-18x)=0
We get rid of parentheses
270x^2+12x-18x=0
We add all the numbers together, and all the variables
270x^2-6x=0
a = 270; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·270·0
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*270}=\frac{0}{540} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*270}=\frac{12}{540} =1/45 $
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