1/10x+520=3/5x

Solution for 1/10x+520=3/5x equation:

1/10x+520=3/5x

We move all terms to the left:

1/10x+520-(3/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x-(+3/5x)+520=0

We get rid of parentheses

1/10x-3/5x+520=0

We calculate fractions


5x/50x^2+(-30x)/50x^2+520=0

We multiply all the terms by the denominator


5x+(-30x)+520*50x^2=0

Wy multiply elements

26000x^2+5x+(-30x)=0

We get rid of parentheses

26000x^2+5x-30x=0

We add all the numbers together, and all the variables

26000x^2-25x=0

a = 26000; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·26000·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*26000}=\frac{0}{52000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*26000}=\frac{50}{52000}
=1/1040
$