-1/3x-2=-1/4x-5

Solution for -1/3x-2=-1/4x-5 equation:

-1/3x-2=-1/4x-5

We move all terms to the left:

-1/3x-2-(-1/4x-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

-1/3x+1/4x+5-2=0

We calculate fractions


(-4x)/12x^2+3x/12x^2+5-2=0

We add all the numbers together, and all the variables

(-4x)/12x^2+3x/12x^2+3=0

We multiply all the terms by the denominator


(-4x)+3x+3*12x^2=0

We add all the numbers together, and all the variables

3x+(-4x)+3*12x^2=0

Wy multiply elements

36x^2+3x+(-4x)=0

We get rid of parentheses

36x^2+3x-4x=0

We add all the numbers together, and all the variables

36x^2-1x=0

a = 36; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·36·0
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*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*36}=\frac{2}{72}
=1/36
$