22=x(x-2)

Solution for 22=x(x-2) equation:

22=x(x-2)

We move all terms to the left:

22-(x(x-2))=0


We calculate terms in parentheses: -(x(x-2)), so:

x(x-2)

We multiply parentheses

x^2-2x

Back to the equation:

-(x^2-2x)


We get rid of parentheses

-x^2+2x+22=0

We add all the numbers together, and all the variables

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

a = -1; b = 2; c = +22;
Δ = b2-4ac
Δ = 22-4·(-1)·22
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{23}}{2*-1}=\frac{-2-2\sqrt{23}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{23}}{2*-1}=\frac{-2+2\sqrt{23}}{-2}
$