1/15x+2=1/20x+4

Solution for 1/15x+2=1/20x+4 equation:

1/15x+2=1/20x+4

We move all terms to the left:

1/15x+2-(1/20x+4)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 20x+4)!=0

x∈R


We get rid of parentheses

1/15x-1/20x-4+2=0

We calculate fractions


20x/300x^2+(-15x)/300x^2-4+2=0

We add all the numbers together, and all the variables

20x/300x^2+(-15x)/300x^2-2=0

We multiply all the terms by the denominator


20x+(-15x)-2*300x^2=0

Wy multiply elements

-600x^2+20x+(-15x)=0

We get rid of parentheses

-600x^2+20x-15x=0

We add all the numbers together, and all the variables

-600x^2+5x=0

a = -600; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-600)·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*-600}=\frac{-10}{-1200}
=1/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-600}=\frac{0}{-1200}
=0
$