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2/5x-3=8-1/3x
We move all terms to the left:
2/5x-3-(8-1/3x)=0
Domain of the equation: 5x!=0
x!=0/5
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
2/5x-(-1/3x+8)-3=0
We get rid of parentheses
2/5x+1/3x-8-3=0
We calculate fractions
6x/15x^2+5x/15x^2-8-3=0
We add all the numbers together, and all the variables
6x/15x^2+5x/15x^2-11=0
We multiply all the terms by the denominator
6x+5x-11*15x^2=0
We add all the numbers together, and all the variables
11x-11*15x^2=0
Wy multiply elements
-165x^2+11x=0
a = -165; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-165)·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-165}=\frac{-22}{-330} =1/15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-165}=\frac{0}{-330} =0 $
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