1/4x-8=1/3x-19

Solution for 1/4x-8=1/3x-19 equation:

1/4x-8=1/3x-19

We move all terms to the left:

1/4x-8-(1/3x-19)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-19)!=0

x∈R


We get rid of parentheses

1/4x-1/3x+19-8=0

We calculate fractions


3x/12x^2+(-4x)/12x^2+19-8=0

We add all the numbers together, and all the variables

3x/12x^2+(-4x)/12x^2+11=0

We multiply all the terms by the denominator


3x+(-4x)+11*12x^2=0

Wy multiply elements

132x^2+3x+(-4x)=0

We get rid of parentheses

132x^2+3x-4x=0

We add all the numbers together, and all the variables

132x^2-1x=0

a = 132; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·132·0
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*132}=\frac{0}{264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*132}=\frac{2}{264}
=1/132
$