3/5x+12=5/7x

Solution for 3/5x+12=5/7x equation:

3/5x+12=5/7x

We move all terms to the left:

3/5x+12-(5/7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(+5/7x)+12=0

We get rid of parentheses

3/5x-5/7x+12=0

We calculate fractions


21x/35x^2+(-25x)/35x^2+12=0

We multiply all the terms by the denominator


21x+(-25x)+12*35x^2=0

Wy multiply elements

420x^2+21x+(-25x)=0

We get rid of parentheses

420x^2+21x-25x=0

We add all the numbers together, and all the variables

420x^2-4x=0

a = 420; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·420·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*420}=\frac{0}{840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*420}=\frac{8}{840}
=1/105
$