2x+36=1/4x

Solution for 2x+36=1/4x equation:

2x+36=1/4x

We move all terms to the left:

2x+36-(1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+1/4x)+36=0

We get rid of parentheses

2x-1/4x+36=0

We multiply all the terms by the denominator


2x*4x+36*4x-1=0

Wy multiply elements

8x^2+144x-1=0

a = 8; b = 144; c = -1;
Δ = b2-4ac
Δ = 1442-4·8·(-1)
Δ = 20768
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:

$\sqrt{\Delta}=\sqrt{20768}=\sqrt{16*1298}=\sqrt{16}*\sqrt{1298}=4\sqrt{1298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1298}}{2*8}=\frac{-144-4\sqrt{1298}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1298}}{2*8}=\frac{-144+4\sqrt{1298}}{16}
$