x(50-2x)=x

Solution for x(50-2x)=x equation:

x(50-2x)=x

We move all terms to the left:

x(50-2x)-(x)=0

We add all the numbers together, and all the variables

x(-2x+50)-x=0

We add all the numbers together, and all the variables

-1x+x(-2x+50)=0

We multiply parentheses

-2x^2-1x+50x=0

We add all the numbers together, and all the variables

-2x^2+49x=0

a = -2; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-2)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-2}=\frac{-98}{-4}
=24+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-2}=\frac{0}{-4}
=0
$