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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

144x^2+3x+(-12x)=0

We get rid of parentheses

144x^2+3x-12x=0

We add all the numbers together, and all the variables

144x^2-9x=0

a = 144; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·144·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*144}=\frac{0}{288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*144}=\frac{18}{288}
=1/16
$