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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

4x/12x^2+(-3x)/12x^2-7=0

We multiply all the terms by the denominator


4x+(-3x)-7*12x^2=0

Wy multiply elements

-84x^2+4x+(-3x)=0

We get rid of parentheses

-84x^2+4x-3x=0

We add all the numbers together, and all the variables

-84x^2+x=0

a = -84; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-84)·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*-84}=\frac{-2}{-168}
=1/84
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-84}=\frac{0}{-168}
=0
$