3/4x=36x=

Solution for 3/4x=36x= equation:

3/4x=36x=

We move all terms to the left:

3/4x-(36x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-36x+3/4x=0

We multiply all the terms by the denominator


-36x*4x+3=0

Wy multiply elements

-144x^2+3=0

a = -144; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-144)·3
Δ = 1728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*-144}=\frac{0-24\sqrt{3}}{-288}
=-\frac{24\sqrt{3}}{-288}
=-\frac{\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*-144}=\frac{0+24\sqrt{3}}{-288}
=\frac{24\sqrt{3}}{-288}
=\frac{\sqrt{3}}{-12}
$