32.5/4.5x-4.5=X

Solution for 32.5/4.5x-4.5=X equation:

32.5/4.5x-4.5=x

We move all terms to the left:

32.5/4.5x-4.5-(x)=0


Domain of the equation: 4.5x!=0

x!=0/4.5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+32.5/4.5x-4.5=0

We multiply all the terms by the denominator


-1x*4.5x-(4.5)*4.5x+32.5=0

We multiply parentheses

-1x*4.5x-18x+32.5=0

Wy multiply elements

-4x^2-18x+32.5=0

a = -4; b = -18; c = +32.5;
Δ = b2-4ac
Δ = -182-4·(-4)·32.5
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{211}}{2*-4}=\frac{18-2\sqrt{211}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{211}}{2*-4}=\frac{18+2\sqrt{211}}{-8}
$