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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-45x^2)/180x^2+72x/180x^2+(-300x)/180x^2=0

We multiply all the terms by the denominator


(-45x^2)+72x+(-300x)=0

We get rid of parentheses

-45x^2+72x-300x=0

We add all the numbers together, and all the variables

-45x^2-228x=0

a = -45; b = -228; c = 0;
Δ = b2-4ac
Δ = -2282-4·(-45)·0
Δ = 51984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51984}=228$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-228}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+228}{2*-45}=\frac{456}{-90}
=-5+1/15
$