32=x-9/5x

Solution for 32=x-9/5x equation:

32=x-9/5x

We move all terms to the left:

32-(x-9/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-9/5x)+32=0

We get rid of parentheses

-x+9/5x+32=0

We multiply all the terms by the denominator


-x*5x+32*5x+9=0

Wy multiply elements

-5x^2+160x+9=0

a = -5; b = 160; c = +9;
Δ = b2-4ac
Δ = 1602-4·(-5)·9
Δ = 25780
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:

$\sqrt{\Delta}=\sqrt{25780}=\sqrt{4*6445}=\sqrt{4}*\sqrt{6445}=2\sqrt{6445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-2\sqrt{6445}}{2*-5}=\frac{-160-2\sqrt{6445}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+2\sqrt{6445}}{2*-5}=\frac{-160+2\sqrt{6445}}{-10}
$