10x=20x-10x^2

Solution for 10x=20x-10x^2 equation:

10x=20x-10x^2

We move all terms to the left:

10x-(20x-10x^2)=0

We get rid of parentheses

10x^2-20x+10x=0

We add all the numbers together, and all the variables

10x^2-10x=0

a = 10; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·10·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*10}=\frac{20}{20}
=1
$