2x(1-x)=5x

Solution for 2x(1-x)=5x equation:

2x(1-x)=5x

We move all terms to the left:

2x(1-x)-(5x)=0

We add all the numbers together, and all the variables

2x(-1x+1)-5x=0

We add all the numbers together, and all the variables

-5x+2x(-1x+1)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-2x^2-3x=0

a = -2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-2)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-2}=\frac{6}{-4}
=-1+1/2
$