57=x(22-x)

Solution for 57=x(22-x) equation:

57=x(22-x)

We move all terms to the left:

57-(x(22-x))=0

We add all the numbers together, and all the variables

-(x(-1x+22))+57=0


We calculate terms in parentheses: -(x(-1x+22)), so:

x(-1x+22)

We multiply parentheses

-1x^2+22x

Back to the equation:

-(-1x^2+22x)


We get rid of parentheses

1x^2-22x+57=0

We add all the numbers together, and all the variables

x^2-22x+57=0

a = 1; b = -22; c = +57;
Δ = b2-4ac
Δ = -222-4·1·57
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-16}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+16}{2*1}=\frac{38}{2}
=19
$