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1/3x+7=3+2/3x.x=
We move all terms to the left:
1/3x+7-(3+2/3x.x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 3x.x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/3x-(2/3x.x+3)+7=0
We get rid of parentheses
1/3x-2/3x.x-3+7=0
We calculate fractions
3x/9x^2+(-6x)/9x^2-3+7=0
We add all the numbers together, and all the variables
3x/9x^2+(-6x)/9x^2+4=0
We multiply all the terms by the denominator
3x+(-6x)+4*9x^2=0
Wy multiply elements
36x^2+3x+(-6x)=0
We get rid of parentheses
36x^2+3x-6x=0
We add all the numbers together, and all the variables
36x^2-3x=0
a = 36; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·36·0
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*36}=\frac{0}{72} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*36}=\frac{6}{72} =1/12 $
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