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2/3x+40=-2/9x
We move all terms to the left:
2/3x+40-(-2/9x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 9x)!=0We get rid of parentheses
x!=0/1
x!=0
x∈R
2/3x+2/9x+40=0
We calculate fractions
18x/27x^2+6x/27x^2+40=0
We multiply all the terms by the denominator
18x+6x+40*27x^2=0
We add all the numbers together, and all the variables
24x+40*27x^2=0
Wy multiply elements
1080x^2+24x=0
a = 1080; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·1080·0
Δ = 576
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{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*1080}=\frac{-48}{2160} =-1/45 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*1080}=\frac{0}{2160} =0 $
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