x(22-x)=8

Solution for x(22-x)=8 equation:

x(22-x)=8

We move all terms to the left:

x(22-x)-(8)=0

We add all the numbers together, and all the variables

x(-1x+22)-8=0

We multiply parentheses

-1x^2+22x-8=0

a = -1; b = 22; c = -8;
Δ = b2-4ac
Δ = 222-4·(-1)·(-8)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{113}}{2*-1}=\frac{-22-2\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{113}}{2*-1}=\frac{-22+2\sqrt{113}}{-2}
$