3/4x=1/12x+6

Solution for 3/4x=1/12x+6 equation:

3/4x=1/12x+6

We move all terms to the left:

3/4x-(1/12x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x+6)!=0

x∈R


We get rid of parentheses

3/4x-1/12x-6=0

We calculate fractions


36x/48x^2+(-4x)/48x^2-6=0

We multiply all the terms by the denominator


36x+(-4x)-6*48x^2=0

Wy multiply elements

-288x^2+36x+(-4x)=0

We get rid of parentheses

-288x^2+36x-4x=0

We add all the numbers together, and all the variables

-288x^2+32x=0

a = -288; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-288)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-288}=\frac{-64}{-576}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-288}=\frac{0}{-576}
=0
$