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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-84x^2-1x=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{0}{-168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-84}=\frac{2}{-168}
=-1/84
$