3/4x-3/20=3/5x

Solution for 3/4x-3/20=3/5x equation:

3/4x-3/20=3/5x

We move all terms to the left:

3/4x-3/20-(3/5x)=0


Domain of the equation: 4x!=0

x!=0/4

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

3/4x-(+3/5x)-3/20=0

We get rid of parentheses

3/4x-3/5x-3/20=0

We calculate fractions


(-300x^2)/800x^2+600x/800x^2+(-480x)/800x^2=0

We multiply all the terms by the denominator


(-300x^2)+600x+(-480x)=0

We get rid of parentheses

-300x^2+600x-480x=0

We add all the numbers together, and all the variables

-300x^2+120x=0

a = -300; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-300)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-300}=\frac{-240}{-600}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-300}=\frac{0}{-600}
=0
$