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2/x-2/3x=1/5
We move all terms to the left:
2/x-2/3x-(1/5)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
2/x-2/3x-(+1/5)=0
We get rid of parentheses
2/x-2/3x-1/5=0
We calculate fractions
(-9x^2)/75x^2+150x/75x^2+(-50x)/75x^2=0
We multiply all the terms by the denominator
(-9x^2)+150x+(-50x)=0
We get rid of parentheses
-9x^2+150x-50x=0
We add all the numbers together, and all the variables
-9x^2+100x=0
a = -9; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-9)·0
Δ = 10000
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{10000}=100$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-9}=\frac{-200}{-18} =11+1/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-9}=\frac{0}{-18} =0 $
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