(13+2x)(11+2x)=217

Solution for (13+2x)(11+2x)=217 equation:

(13+2x)(11+2x)=217

We move all terms to the left:

(13+2x)(11+2x)-(217)=0

We add all the numbers together, and all the variables

(2x+13)(2x+11)-217=0

We multiply parentheses ..

(+4x^2+22x+26x+143)-217=0

We get rid of parentheses

4x^2+22x+26x+143-217=0

We add all the numbers together, and all the variables

4x^2+48x-74=0

a = 4; b = 48; c = -74;
Δ = b2-4ac
Δ = 482-4·4·(-74)
Δ = 3488
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:

$\sqrt{\Delta}=\sqrt{3488}=\sqrt{16*218}=\sqrt{16}*\sqrt{218}=4\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{218}}{2*4}=\frac{-48-4\sqrt{218}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{218}}{2*4}=\frac{-48+4\sqrt{218}}{8}
$