1/3x-8=12+3/4x

Solution for 1/3x-8=12+3/4x equation:

1/3x-8=12+3/4x

We move all terms to the left:

1/3x-8-(12+3/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(3/4x+12)-8=0

We get rid of parentheses

1/3x-3/4x-12-8=0

We calculate fractions


4x/12x^2+(-9x)/12x^2-12-8=0

We add all the numbers together, and all the variables

4x/12x^2+(-9x)/12x^2-20=0

We multiply all the terms by the denominator


4x+(-9x)-20*12x^2=0

Wy multiply elements

-240x^2+4x+(-9x)=0

We get rid of parentheses

-240x^2+4x-9x=0

We add all the numbers together, and all the variables

-240x^2-5x=0

a = -240; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-240)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-240}=\frac{0}{-480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-240}=\frac{10}{-480}
=-1/48
$