3/5x-1/2x=13/20

Solution for 3/5x-1/2x=13/20 equation:

3/5x-1/2x=13/20

We move all terms to the left:

3/5x-1/2x-(13/20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-1/2x-(+13/20)=0

We get rid of parentheses

3/5x-1/2x-13/20=0

We calculate fractions


(-260x^2)/400x^2+240x/400x^2+(-200x)/400x^2=0

We multiply all the terms by the denominator


(-260x^2)+240x+(-200x)=0

We get rid of parentheses

-260x^2+240x-200x=0

We add all the numbers together, and all the variables

-260x^2+40x=0

a = -260; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-260)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-260}=\frac{-80}{-520}
=2/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-260}=\frac{0}{-520}
=0
$