(17+2x)(11+2x)=80

Solution for (17+2x)(11+2x)=80 equation:

(17+2x)(11+2x)=80

We move all terms to the left:

(17+2x)(11+2x)-(80)=0

We add all the numbers together, and all the variables

(2x+17)(2x+11)-80=0

We multiply parentheses ..

(+4x^2+22x+34x+187)-80=0

We get rid of parentheses

4x^2+22x+34x+187-80=0

We add all the numbers together, and all the variables

4x^2+56x+107=0

a = 4; b = 56; c = +107;
Δ = b2-4ac
Δ = 562-4·4·107
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{89}}{2*4}=\frac{-56-4\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{89}}{2*4}=\frac{-56+4\sqrt{89}}{8}
$