2/36x+3)=4x+2

Solution for 2/36x+3)=4x+2 equation:

2/36x+3)=4x+2

We move all terms to the left:

2/36x+3)-(4x+2)=0


Domain of the equation: 36x!=0

x!=0/36

x!=0

x∈R


We add all the numbers together, and all the variables

2/36x+3)-(4x=0

We multiply all the terms by the denominator


-4x*36x+2+3=0

We add all the numbers together, and all the variables

-4x*36x+5=0

Wy multiply elements

-144x^2+5=0

a = -144; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-144)·5
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*-144}=\frac{0-24\sqrt{5}}{-288}
=-\frac{24\sqrt{5}}{-288}
=-\frac{\sqrt{5}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*-144}=\frac{0+24\sqrt{5}}{-288}
=\frac{24\sqrt{5}}{-288}
=\frac{\sqrt{5}}{-12}
$