3x-472=4/x

Solution for 3x-472=4/x equation:

3x-472=4/x

We move all terms to the left:

3x-472-(4/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-(+4/x)-472=0

We get rid of parentheses

3x-4/x-472=0

We multiply all the terms by the denominator


3x*x-472*x-4=0

We add all the numbers together, and all the variables

-472x+3x*x-4=0

Wy multiply elements

3x^2-472x-4=0

a = 3; b = -472; c = -4;
Δ = b2-4ac
Δ = -4722-4·3·(-4)
Δ = 222832
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:

$\sqrt{\Delta}=\sqrt{222832}=\sqrt{16*13927}=\sqrt{16}*\sqrt{13927}=4\sqrt{13927}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-472)-4\sqrt{13927}}{2*3}=\frac{472-4\sqrt{13927}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-472)+4\sqrt{13927}}{2*3}=\frac{472+4\sqrt{13927}}{6}
$