(4/x)=x+3

Solution for (4/x)=x+3 equation:

(4/x)=x+3

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/x-x-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x-x*x+4=0

Wy multiply elements

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

a = -1; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-1}=\frac{8}{-2}
=-4
$