X+4=165/x

Solution for X+4=165/x equation:

X+4=165/X

We move all terms to the left:

X+4-(165/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

X-(+165/X)+4=0

We get rid of parentheses

X-165/X+4=0

We multiply all the terms by the denominator


X*X+4*X-165=0

We add all the numbers together, and all the variables

4X+X*X-165=0

Wy multiply elements

X^2+4X-165=0

a = 1; b = 4; c = -165;
Δ = b2-4ac
Δ = 42-4·1·(-165)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-26}{2*1}=\frac{-30}{2}
=-15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+26}{2*1}=\frac{22}{2}
=11
$