2x(10-x)=25

Solution for 2x(10-x)=25 equation:

2x(10-x)=25

We move all terms to the left:

2x(10-x)-(25)=0

We add all the numbers together, and all the variables

2x(-1x+10)-25=0

We multiply parentheses

-2x^2+20x-25=0

a = -2; b = 20; c = -25;
Δ = b2-4ac
Δ = 202-4·(-2)·(-25)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{2}}{2*-2}=\frac{-20-10\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{2}}{2*-2}=\frac{-20+10\sqrt{2}}{-4}
$