4/x=x-21

Solution for 4/x=x-21 equation:

4/x=x-21

We move all terms to the left:

4/x-(x-21)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-x+21=0

We multiply all the terms by the denominator


-x*x+21*x+4=0

We add all the numbers together, and all the variables

21x-x*x+4=0

Wy multiply elements

-1x^2+21x+4=0

a = -1; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·(-1)·4
Δ = 457
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{457}}{2*-1}=\frac{-21-\sqrt{457}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{457}}{2*-1}=\frac{-21+\sqrt{457}}{-2}
$