2=10x-5x^2

Solution for 2=10x-5x^2 equation:

2=10x-5x^2

We move all terms to the left:

2-(10x-5x^2)=0

We get rid of parentheses

5x^2-10x+2=0

a = 5; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·5·2
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*5}=\frac{10-2\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*5}=\frac{10+2\sqrt{15}}{10}
$