3/4x=3/5x-12

Solution for 3/4x=3/5x-12 equation:

3/4x=3/5x-12

We move all terms to the left:

3/4x-(3/5x-12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x-12)!=0

x∈R


We get rid of parentheses

3/4x-3/5x+12=0

We calculate fractions


15x/20x^2+(-12x)/20x^2+12=0

We multiply all the terms by the denominator


15x+(-12x)+12*20x^2=0

Wy multiply elements

240x^2+15x+(-12x)=0

We get rid of parentheses

240x^2+15x-12x=0

We add all the numbers together, and all the variables

240x^2+3x=0

a = 240; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·240·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*240}=\frac{-6}{480}
=-1/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*240}=\frac{0}{480}
=0
$