3/8x-15=6/5x+12

Solution for 3/8x-15=6/5x+12 equation:

3/8x-15=6/5x+12

We move all terms to the left:

3/8x-15-(6/5x+12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/8x-6/5x-12-15=0

We calculate fractions


15x/40x^2+(-48x)/40x^2-12-15=0

We add all the numbers together, and all the variables

15x/40x^2+(-48x)/40x^2-27=0

We multiply all the terms by the denominator


15x+(-48x)-27*40x^2=0

Wy multiply elements

-1080x^2+15x+(-48x)=0

We get rid of parentheses

-1080x^2+15x-48x=0

We add all the numbers together, and all the variables

-1080x^2-33x=0

a = -1080; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·(-1080)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*-1080}=\frac{0}{-2160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*-1080}=\frac{66}{-2160}
=-11/360
$