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2/5x-3=4/x
We move all terms to the left:
2/5x-3-(4/x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/5x-(+4/x)-3=0
We get rid of parentheses
2/5x-4/x-3=0
We calculate fractions
2x/5x^2+(-20x)/5x^2-3=0
We multiply all the terms by the denominator
2x+(-20x)-3*5x^2=0
Wy multiply elements
-15x^2+2x+(-20x)=0
We get rid of parentheses
-15x^2+2x-20x=0
We add all the numbers together, and all the variables
-15x^2-18x=0
a = -15; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-15)·0
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-15}=\frac{0}{-30} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-15}=\frac{36}{-30} =-1+1/5 $
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