3/x=x+4

Solution for 3/x=x+4 equation:

3/x=x+4

We move all terms to the left:

3/x-(x+4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3/x-x-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x-x*x+3=0

Wy multiply elements

-1x^2-4x+3=0

a = -1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-1)·3
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{7}}{2*-1}=\frac{4-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{7}}{2*-1}=\frac{4+2\sqrt{7}}{-2}
$