324/x=4.x

Solution for 324/x=4.x equation:

324/x=4.x

We move all terms to the left:

324/x-(4.x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

324/x-(+4.x)=0

We get rid of parentheses

324/x-4.x=0

We multiply all the terms by the denominator


-(4.x)*x+324=0

We add all the numbers together, and all the variables

-(+4.x)*x+324=0

We multiply parentheses

-4x^2+324=0

a = -4; b = 0; c = +324;
Δ = b2-4ac
Δ = 02-4·(-4)·324
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*-4}=\frac{-72}{-8}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*-4}=\frac{72}{-8}
=-9
$