(X+4)(x+8)=165

Solution for (X+4)(x+8)=165 equation:

(X+4)(X+8)=165

We move all terms to the left:

(X+4)(X+8)-(165)=0

We multiply parentheses ..

(+X^2+8X+4X+32)-165=0

We get rid of parentheses

X^2+8X+4X+32-165=0

We add all the numbers together, and all the variables

X^2+12X-133=0

a = 1; b = 12; c = -133;
Δ = b2-4ac
Δ = 122-4·1·(-133)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-26}{2*1}=\frac{-38}{2}
=-19
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+26}{2*1}=\frac{14}{2}
=7
$