3x=432/x

Solution for 3x=432/x equation:

3x=432/x

We move all terms to the left:

3x-(432/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+432/x)=0

We get rid of parentheses

3x-432/x=0

We multiply all the terms by the denominator


3x*x-432=0

Wy multiply elements

3x^2-432=0

a = 3; b = 0; c = -432;
Δ = b2-4ac
Δ = 02-4·3·(-432)
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*3}=\frac{-72}{6}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*3}=\frac{72}{6}
=12
$