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1/3x-2=1/5x
We move all terms to the left:
1/3x-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)-2=0
We get rid of parentheses
1/3x-1/5x-2=0
We calculate fractions
5x/15x^2+(-3x)/15x^2-2=0
We multiply all the terms by the denominator
5x+(-3x)-2*15x^2=0
Wy multiply elements
-30x^2+5x+(-3x)=0
We get rid of parentheses
-30x^2+5x-3x=0
We add all the numbers together, and all the variables
-30x^2+2x=0
a = -30; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-30)·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-30}=\frac{-4}{-60} =1/15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-30}=\frac{0}{-60} =0 $
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