2/5x-1=3/10x+5

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Solution for 2/5x-1=3/10x+5 equation:



2/5x-1=3/10x+5
We move all terms to the left:
2/5x-1-(3/10x+5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x+5)!=0
x∈R
We get rid of parentheses
2/5x-3/10x-5-1=0
We calculate fractions
20x/50x^2+(-15x)/50x^2-5-1=0
We add all the numbers together, and all the variables
20x/50x^2+(-15x)/50x^2-6=0
We multiply all the terms by the denominator
20x+(-15x)-6*50x^2=0
Wy multiply elements
-300x^2+20x+(-15x)=0
We get rid of parentheses
-300x^2+20x-15x=0
We add all the numbers together, and all the variables
-300x^2+5x=0
a = -300; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-300)·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*-300}=\frac{-10}{-600} =1/60 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-300}=\frac{0}{-600} =0 $

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