1/3x-5=2/5x+12

Solution for 1/3x-5=2/5x+12 equation:

1/3x-5=2/5x+12

We move all terms to the left:

1/3x-5-(2/5x+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/3x-2/5x-12-5=0

We calculate fractions


5x/15x^2+(-6x)/15x^2-12-5=0

We add all the numbers together, and all the variables

5x/15x^2+(-6x)/15x^2-17=0

We multiply all the terms by the denominator


5x+(-6x)-17*15x^2=0

Wy multiply elements

-255x^2+5x+(-6x)=0

We get rid of parentheses

-255x^2+5x-6x=0

We add all the numbers together, and all the variables

-255x^2-1x=0

a = -255; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-255)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-255}=\frac{0}{-510}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-255}=\frac{2}{-510}
=-1/255
$