(260-2x)*x=x

Solution for (260-2x)*x=x equation:

(260-2x)*x=x

We move all terms to the left:

(260-2x)*x-(x)=0

We add all the numbers together, and all the variables

(-2x+260)*x-x=0

We add all the numbers together, and all the variables

-1x+(-2x+260)*x=0

We multiply parentheses

-2x^2-1x+260x=0

We add all the numbers together, and all the variables

-2x^2+259x=0

a = -2; b = 259; c = 0;
Δ = b2-4ac
Δ = 2592-4·(-2)·0
Δ = 67081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67081}=259$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(259)-259}{2*-2}=\frac{-518}{-4}
=129+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(259)+259}{2*-2}=\frac{0}{-4}
=0
$