54=(x+2)(x+3)

Solution for 54=(x+2)(x+3) equation:

54=(x+2)(x+3)

We move all terms to the left:

54-((x+2)(x+3))=0

We multiply parentheses ..

-((+x^2+3x+2x+6))+54=0


We calculate terms in parentheses: -((+x^2+3x+2x+6)), so:

(+x^2+3x+2x+6)

We get rid of parentheses

x^2+3x+2x+6

We add all the numbers together, and all the variables

x^2+5x+6

Back to the equation:

-(x^2+5x+6)


We get rid of parentheses

-x^2-5x-6+54=0

We add all the numbers together, and all the variables

-1x^2-5x+48=0

a = -1; b = -5; c = +48;
Δ = b2-4ac
Δ = -52-4·(-1)·48
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{217}}{2*-1}=\frac{5-\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*-1}=\frac{5+\sqrt{217}}{-2}
$