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(-4.5)!=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)+32.5=0

Wy multiply elements

-4x^2+32.5=0

a = -4; b = 0; c = +32.5;
Δ = b2-4ac
Δ = 02-4·(-4)·32.5
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{130}}{2*-4}=\frac{0-2\sqrt{130}}{-8}
=-\frac{2\sqrt{130}}{-8}
=-\frac{\sqrt{130}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{130}}{2*-4}=\frac{0+2\sqrt{130}}{-8}
=\frac{2\sqrt{130}}{-8}
=\frac{\sqrt{130}}{-4}
$