466=3x-3/x

Solution for 466=3x-3/x equation:

466=3x-3/x

We move all terms to the left:

466-(3x-3/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-3/x)+466=0

We get rid of parentheses

-3x+3/x+466=0

We multiply all the terms by the denominator


-3x*x+466*x+3=0

We add all the numbers together, and all the variables

466x-3x*x+3=0

Wy multiply elements

-3x^2+466x+3=0

a = -3; b = 466; c = +3;
Δ = b2-4ac
Δ = 4662-4·(-3)·3
Δ = 217192
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:

$\sqrt{\Delta}=\sqrt{217192}=\sqrt{4*54298}=\sqrt{4}*\sqrt{54298}=2\sqrt{54298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(466)-2\sqrt{54298}}{2*-3}=\frac{-466-2\sqrt{54298}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(466)+2\sqrt{54298}}{2*-3}=\frac{-466+2\sqrt{54298}}{-6}
$