1/36x+30)=4x+20

Solution for 1/36x+30)=4x+20 equation:

1/36x+30)=4x+20

We move all terms to the left:

1/36x+30)-(4x+20)=0


Domain of the equation: 36x!=0

x!=0/36

x!=0

x∈R


We add all the numbers together, and all the variables

1/36x+30)-(4x=0

We multiply all the terms by the denominator


-4x*36x+1+30=0

We add all the numbers together, and all the variables

-4x*36x+31=0

Wy multiply elements

-144x^2+31=0

a = -144; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-144)·31
Δ = 17856
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:

$\sqrt{\Delta}=\sqrt{17856}=\sqrt{576*31}=\sqrt{576}*\sqrt{31}=24\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{31}}{2*-144}=\frac{0-24\sqrt{31}}{-288}
=-\frac{24\sqrt{31}}{-288}
=-\frac{\sqrt{31}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{31}}{2*-144}=\frac{0+24\sqrt{31}}{-288}
=\frac{24\sqrt{31}}{-288}
=\frac{\sqrt{31}}{-12}
$