X-4=21/x

Solution for X-4=21/x equation:

X-4=21/X

We move all terms to the left:

X-4-(21/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-(+21/X)-4=0

We get rid of parentheses

X-21/X-4=0

We multiply all the terms by the denominator


X*X-4*X-21=0

We add all the numbers together, and all the variables

-4X+X*X-21=0

Wy multiply elements

X^2-4X-21=0

a = 1; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*1}=\frac{14}{2}
=7
$