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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4x)+1)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


12x*4x)+1)-(12(-4*4x)+1)+3=0

Wy multiply elements

48x^2-16x=0

a = 48; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·48·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*48}=\frac{32}{96}
=1/3
$