(X+6)(x+2)=221

Solution for (X+6)(x+2)=221 equation:

(X+6)(X+2)=221

We move all terms to the left:

(X+6)(X+2)-(221)=0

We multiply parentheses ..

(+X^2+2X+6X+12)-221=0

We get rid of parentheses

X^2+2X+6X+12-221=0

We add all the numbers together, and all the variables

X^2+8X-209=0

a = 1; b = 8; c = -209;
Δ = b2-4ac
Δ = 82-4·1·(-209)
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{-(8)-30}{2*1}=\frac{-38}{2}
=-19
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+30}{2*1}=\frac{22}{2}
=11
$