x(25-x)=50

Solution for x(25-x)=50 equation:

x(25-x)=50

We move all terms to the left:

x(25-x)-(50)=0

We add all the numbers together, and all the variables

x(-1x+25)-50=0

We multiply parentheses

-1x^2+25x-50=0

a = -1; b = 25; c = -50;
Δ = b2-4ac
Δ = 252-4·(-1)·(-50)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{17}}{2*-1}=\frac{-25-5\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{17}}{2*-1}=\frac{-25+5\sqrt{17}}{-2}
$