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1/3*2x+4+5=2/3x+1
We move all terms to the left:
1/3*2x+4+5-(2/3x+1)=0
Domain of the equation: 3*2x!=0
x!=0/1
x!=0
x∈R
Domain of the equation: 3x+1)!=0We add all the numbers together, and all the variables
x∈R
1/3*2x-(2/3x+1)+9=0
We get rid of parentheses
1/3*2x-2/3x-1+9=0
We calculate fractions
3x/54x^2+(-24x)/54x^2-1+9=0
We add all the numbers together, and all the variables
3x/54x^2+(-24x)/54x^2+8=0
We multiply all the terms by the denominator
3x+(-24x)+8*54x^2=0
Wy multiply elements
432x^2+3x+(-24x)=0
We get rid of parentheses
432x^2+3x-24x=0
We add all the numbers together, and all the variables
432x^2-21x=0
a = 432; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·432·0
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*432}=\frac{0}{864} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*432}=\frac{42}{864} =7/144 $
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