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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/15x^2+(-10x)/15x^2+5-12=0

We add all the numbers together, and all the variables

3x/15x^2+(-10x)/15x^2-7=0

We multiply all the terms by the denominator


3x+(-10x)-7*15x^2=0

Wy multiply elements

-105x^2+3x+(-10x)=0

We get rid of parentheses

-105x^2+3x-10x=0

We add all the numbers together, and all the variables

-105x^2-7x=0

a = -105; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-105)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-105}=\frac{0}{-210}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-105}=\frac{14}{-210}
=-1/15
$