4+1/36*x=1/12*x

Solution for 4+1/36*x=1/12*x equation:

4+1/36x=1/12x

We move all terms to the left:

4+1/36x-(1/12x)=0


Domain of the equation: 36x!=0

x!=0/36

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/36x-(+1/12x)+4=0

We get rid of parentheses

1/36x-1/12x+4=0

We calculate fractions


12x/432x^2+(-36x)/432x^2+4=0

We multiply all the terms by the denominator


12x+(-36x)+4*432x^2=0

Wy multiply elements

1728x^2+12x+(-36x)=0

We get rid of parentheses

1728x^2+12x-36x=0

We add all the numbers together, and all the variables

1728x^2-24x=0

a = 1728; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·1728·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*1728}=\frac{0}{3456}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*1728}=\frac{48}{3456}
=1/72
$