18x=1/4x

Solution for 18x=1/4x equation:

18x=1/4x

We move all terms to the left:

18x-(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

18x-(+1/4x)=0

We get rid of parentheses

18x-1/4x=0

We multiply all the terms by the denominator


18x*4x-1=0

Wy multiply elements

72x^2-1=0

a = 72; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·72·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*72}=\frac{0-12\sqrt{2}}{144}
=-\frac{12\sqrt{2}}{144}
=-\frac{\sqrt{2}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*72}=\frac{0+12\sqrt{2}}{144}
=\frac{12\sqrt{2}}{144}
=\frac{\sqrt{2}}{12}
$