x-162=1/4x

Solution for x-162=1/4x equation:

x-162=1/4x

We move all terms to the left:

x-162-(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)-162=0

We get rid of parentheses

x-1/4x-162=0

We multiply all the terms by the denominator


x*4x-162*4x-1=0

Wy multiply elements

4x^2-648x-1=0

a = 4; b = -648; c = -1;
Δ = b2-4ac
Δ = -6482-4·4·(-1)
Δ = 419920
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:

$\sqrt{\Delta}=\sqrt{419920}=\sqrt{16*26245}=\sqrt{16}*\sqrt{26245}=4\sqrt{26245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-4\sqrt{26245}}{2*4}=\frac{648-4\sqrt{26245}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+4\sqrt{26245}}{2*4}=\frac{648+4\sqrt{26245}}{8}
$