(x+5)(2x+16)=1

Solution for (x+5)(2x+16)=1 equation:

(x+5)(2x+16)=1

We move all terms to the left:

(x+5)(2x+16)-(1)=0

We multiply parentheses ..

(+2x^2+16x+10x+80)-1=0

We get rid of parentheses

2x^2+16x+10x+80-1=0

We add all the numbers together, and all the variables

2x^2+26x+79=0

a = 2; b = 26; c = +79;
Δ = b2-4ac
Δ = 262-4·2·79
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{11}}{2*2}=\frac{-26-2\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{11}}{2*2}=\frac{-26+2\sqrt{11}}{4}
$