1/9x+20.5+25.5=x

Solution for 1/9x+20.5+25.5=x equation:

1/9x+20.5+25.5=x

We move all terms to the left:

1/9x+20.5+25.5-(x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/9x+46=0

We multiply all the terms by the denominator


-1x*9x+46*9x+1=0

Wy multiply elements

-9x^2+414x+1=0

a = -9; b = 414; c = +1;
Δ = b2-4ac
Δ = 4142-4·(-9)·1
Δ = 171432
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:

$\sqrt{\Delta}=\sqrt{171432}=\sqrt{36*4762}=\sqrt{36}*\sqrt{4762}=6\sqrt{4762}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(414)-6\sqrt{4762}}{2*-9}=\frac{-414-6\sqrt{4762}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(414)+6\sqrt{4762}}{2*-9}=\frac{-414+6\sqrt{4762}}{-18}
$