x+13+221=(x+13)(x+2)

Solution for x+13+221=(x+13)(x+2) equation:

x+13+221=(x+13)(x+2)

We move all terms to the left:

x+13+221-((x+13)(x+2))=0

We add all the numbers together, and all the variables

x-((x+13)(x+2))+234=0

We multiply parentheses ..

-((+x^2+2x+13x+26))+x+234=0


We calculate terms in parentheses: -((+x^2+2x+13x+26)), so:

(+x^2+2x+13x+26)

We get rid of parentheses

x^2+2x+13x+26

We add all the numbers together, and all the variables

x^2+15x+26

Back to the equation:

-(x^2+15x+26)


We add all the numbers together, and all the variables

x-(x^2+15x+26)+234=0

We get rid of parentheses

-x^2+x-15x-26+234=0

We add all the numbers together, and all the variables

-1x^2-14x+208=0

a = -1; b = -14; c = +208;
Δ = b2-4ac
Δ = -142-4·(-1)·208
Δ = 1028
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:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{257}}{2*-1}=\frac{14-2\sqrt{257}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{257}}{2*-1}=\frac{14+2\sqrt{257}}{-2}
$