-1/3x-8=-1/4x-3

Solution for -1/3x-8=-1/4x-3 equation:

-1/3x-8=-1/4x-3

We move all terms to the left:

-1/3x-8-(-1/4x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

-1/3x+1/4x+3-8=0

We calculate fractions


(-4x)/12x^2+3x/12x^2+3-8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-60x^2+3x+(-4x)=0

We get rid of parentheses

-60x^2+3x-4x=0

We add all the numbers together, and all the variables

-60x^2-1x=0

a = -60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-60}=\frac{2}{-120}
=-1/60
$