3/4x-15=6/5x-12

Solution for 3/4x-15=6/5x-12 equation:

3/4x-15=6/5x-12

We move all terms to the left:

3/4x-15-(6/5x-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-6/5x+12-15=0

We calculate fractions


15x/20x^2+(-24x)/20x^2+12-15=0

We add all the numbers together, and all the variables

15x/20x^2+(-24x)/20x^2-3=0

We multiply all the terms by the denominator


15x+(-24x)-3*20x^2=0

Wy multiply elements

-60x^2+15x+(-24x)=0

We get rid of parentheses

-60x^2+15x-24x=0

We add all the numbers together, and all the variables

-60x^2-9x=0

a = -60; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-60)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-60}=\frac{18}{-120}
=-3/20
$