2x=338/x

Solution for 2x=338/x equation:

2x=338/x

We move all terms to the left:

2x-(338/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

2x-(+338/x)=0

We get rid of parentheses

2x-338/x=0

We multiply all the terms by the denominator


2x*x-338=0

Wy multiply elements

2x^2-338=0

a = 2; b = 0; c = -338;
Δ = b2-4ac
Δ = 02-4·2·(-338)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52}{2*2}=\frac{-52}{4}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52}{2*2}=\frac{52}{4}
=13
$