(x+4)(x+8)=221

Solution for (x+4)(x+8)=221 equation:

(x+4)(x+8)=221

We move all terms to the left:

(x+4)(x+8)-(221)=0

We multiply parentheses ..

(+x^2+8x+4x+32)-221=0

We get rid of parentheses

x^2+8x+4x+32-221=0

We add all the numbers together, and all the variables

x^2+12x-189=0

a = 1; b = 12; c = -189;
Δ = b2-4ac
Δ = 122-4·1·(-189)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-30}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+30}{2*1}=\frac{18}{2}
=9
$