7/x=21-x

Solution for 7/x=21-x equation:

7/x=21-x

We move all terms to the left:

7/x-(21-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7/x-(-1x+21)=0

We get rid of parentheses

7/x+1x-21=0

We multiply all the terms by the denominator


1x*x-21*x+7=0

We add all the numbers together, and all the variables

-21x+1x*x+7=0

Wy multiply elements

x^2-21x+7=0

a = 1; b = -21; c = +7;
Δ = b2-4ac
Δ = -212-4·1·7
Δ = 413
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{413}}{2*1}=\frac{21-\sqrt{413}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{413}}{2*1}=\frac{21+\sqrt{413}}{2}
$