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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+x^2+2x+13x+26))+13x+221=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

13x-(x^2+15x+26)+221=0

We get rid of parentheses

-x^2+13x-15x-26+221=0

We add all the numbers together, and all the variables

-1x^2-2x+195=0

a = -1; b = -2; c = +195;
Δ = b2-4ac
Δ = -22-4·(-1)·195
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-28}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+28}{2*-1}=\frac{30}{-2}
=-15
$