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1/x+1/2x=1/5
We move all terms to the left:
1/x+1/2x-(1/5)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
1/x+1/2x-(+1/5)=0
We get rid of parentheses
1/x+1/2x-1/5=0
We calculate fractions
(-4x^2)/50x^2+50x/50x^2+25x/50x^2=0
We multiply all the terms by the denominator
(-4x^2)+50x+25x=0
We add all the numbers together, and all the variables
(-4x^2)+75x=0
We get rid of parentheses
-4x^2+75x=0
a = -4; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-4)·0
Δ = 5625
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{5625}=75$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-4}=\frac{-150}{-8} =18+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-4}=\frac{0}{-8} =0 $
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