X+36=1/4x

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

X+36=1/4X

We move all terms to the left:

X+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

X-(+1/4X)+36=0

We get rid of parentheses

X-1/4X+36=0

We multiply all the terms by the denominator


X*4X+36*4X-1=0

Wy multiply elements

4X^2+144X-1=0

a = 4; b = 144; c = -1;
Δ = b2-4ac
Δ = 1442-4·4·(-1)
Δ = 20752
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:

$\sqrt{\Delta}=\sqrt{20752}=\sqrt{16*1297}=\sqrt{16}*\sqrt{1297}=4\sqrt{1297}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1297}}{2*4}=\frac{-144-4\sqrt{1297}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1297}}{2*4}=\frac{-144+4\sqrt{1297}}{8}
$