2=20x-10x^2

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

2=20x-10x^2

We move all terms to the left:

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

We get rid of parentheses

10x^2-20x+2=0

a = 10; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·10·2
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{5}}{2*10}=\frac{20-8\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{5}}{2*10}=\frac{20+8\sqrt{5}}{20}
$