(42/x)+x=21

Solution for (42/x)+x=21 equation:

(42/x)+x=21

We move all terms to the left:

(42/x)+x-(21)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+42/x)+x-21=0

We add all the numbers together, and all the variables

x+(+42/x)-21=0

We get rid of parentheses

x+42/x-21=0

We multiply all the terms by the denominator


x*x-21*x+42=0

We add all the numbers together, and all the variables

-21x+x*x+42=0

Wy multiply elements

x^2-21x+42=0

a = 1; b = -21; c = +42;
Δ = b2-4ac
Δ = -212-4·1·42
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{273}}{2*1}=\frac{21-\sqrt{273}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{273}}{2*1}=\frac{21+\sqrt{273}}{2}
$