55=(x-2)(x+4)

Solution for 55=(x-2)(x+4) equation:

55=(x-2)(x+4)

We move all terms to the left:

55-((x-2)(x+4))=0

We multiply parentheses ..

-((+x^2+4x-2x-8))+55=0


We calculate terms in parentheses: -((+x^2+4x-2x-8)), so:

(+x^2+4x-2x-8)

We get rid of parentheses

x^2+4x-2x-8

We add all the numbers together, and all the variables

x^2+2x-8

Back to the equation:

-(x^2+2x-8)


We get rid of parentheses

-x^2-2x+8+55=0

We add all the numbers together, and all the variables

-1x^2-2x+63=0

a = -1; b = -2; c = +63;
Δ = b2-4ac
Δ = -22-4·(-1)·63
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{-(-2)-16}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*-1}=\frac{18}{-2}
=-9
$