3600/5x=x

Solution for 3600/5x=x equation:

3600/5x=x

We move all terms to the left:

3600/5x-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3600/5x=0

We multiply all the terms by the denominator


-1x*5x+3600=0

Wy multiply elements

-5x^2+3600=0

a = -5; b = 0; c = +3600;
Δ = b2-4ac
Δ = 02-4·(-5)·3600
Δ = 72000
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:

$\sqrt{\Delta}=\sqrt{72000}=\sqrt{14400*5}=\sqrt{14400}*\sqrt{5}=120\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{5}}{2*-5}=\frac{0-120\sqrt{5}}{-10}
=-\frac{120\sqrt{5}}{-10}
=-\frac{12\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{5}}{2*-5}=\frac{0+120\sqrt{5}}{-10}
=\frac{120\sqrt{5}}{-10}
=\frac{12\sqrt{5}}{-1}
$