x-27=1/4x

Solution for x-27=1/4x equation:

x-27=1/4x

We move all terms to the left:

x-27-(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)-27=0

We get rid of parentheses

x-1/4x-27=0

We multiply all the terms by the denominator


x*4x-27*4x-1=0

Wy multiply elements

4x^2-108x-1=0

a = 4; b = -108; c = -1;
Δ = b2-4ac
Δ = -1082-4·4·(-1)
Δ = 11680
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:

$\sqrt{\Delta}=\sqrt{11680}=\sqrt{16*730}=\sqrt{16}*\sqrt{730}=4\sqrt{730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{730}}{2*4}=\frac{108-4\sqrt{730}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{730}}{2*4}=\frac{108+4\sqrt{730}}{8}
$