x-21=2/9.x

Solution for x-21=2/9.x equation:

x-21=2/9.x

We move all terms to the left:

x-21-(2/9.x)=0


Domain of the equation: 9.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+2/9.x)-21=0

We get rid of parentheses

x-2/9.x-21=0

We multiply all the terms by the denominator


x*9.x-21*9.x-2=0

Wy multiply elements

9x^2-189x-2=0

a = 9; b = -189; c = -2;
Δ = b2-4ac
Δ = -1892-4·9·(-2)
Δ = 35793
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:

$\sqrt{\Delta}=\sqrt{35793}=\sqrt{9*3977}=\sqrt{9}*\sqrt{3977}=3\sqrt{3977}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-3\sqrt{3977}}{2*9}=\frac{189-3\sqrt{3977}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+3\sqrt{3977}}{2*9}=\frac{189+3\sqrt{3977}}{18}
$