21/(x-24)=x

Solution for 21/(x-24)=x equation:

21/(x-24)=x

We move all terms to the left:

21/(x-24)-(x)=0


Domain of the equation: (x-24)!=0

We move all terms containing x to the left, all other terms to the right

x!=24

x∈R


We add all the numbers together, and all the variables

-1x+21/(x-24)=0

We multiply all the terms by the denominator


-1x*(x-24)+21=0

We multiply parentheses

-x^2+24x+21=0

We add all the numbers together, and all the variables

-1x^2+24x+21=0

a = -1; b = 24; c = +21;
Δ = b2-4ac
Δ = 242-4·(-1)·21
Δ = 660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{165}}{2*-1}=\frac{-24-2\sqrt{165}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{165}}{2*-1}=\frac{-24+2\sqrt{165}}{-2}
$