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1/3x+1/2=1/5x
We move all terms to the left:
1/3x+1/2-(1/5x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/3x-(+1/5x)+1/2=0
We get rid of parentheses
1/3x-1/5x+1/2=0
We calculate fractions
75x^2/60x^2+20x/60x^2+(-12x)/60x^2=0
We multiply all the terms by the denominator
75x^2+20x+(-12x)=0
We get rid of parentheses
75x^2+20x-12x=0
We add all the numbers together, and all the variables
75x^2+8x=0
a = 75; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·75·0
Δ = 64
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{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*75}=\frac{-16}{150} =-8/75 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*75}=\frac{0}{150} =0 $
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