1+1/5x=3/10x

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Solution for 1+1/5x=3/10x equation:



1+1/5x=3/10x
We move all terms to the left:
1+1/5x-(3/10x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/5x-(+3/10x)+1=0
We get rid of parentheses
1/5x-3/10x+1=0
We calculate fractions
10x/50x^2+(-15x)/50x^2+1=0
We multiply all the terms by the denominator
10x+(-15x)+1*50x^2=0
Wy multiply elements
50x^2+10x+(-15x)=0
We get rid of parentheses
50x^2+10x-15x=0
We add all the numbers together, and all the variables
50x^2-5x=0
a = 50; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·50·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*50}=\frac{0}{100} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*50}=\frac{10}{100} =1/10 $

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