(17+2x)(11+2x)=391

Solution for (17+2x)(11+2x)=391 equation:

(17+2x)(11+2x)=391

We move all terms to the left:

(17+2x)(11+2x)-(391)=0

We add all the numbers together, and all the variables

(2x+17)(2x+11)-391=0

We multiply parentheses ..

(+4x^2+22x+34x+187)-391=0

We get rid of parentheses

4x^2+22x+34x+187-391=0

We add all the numbers together, and all the variables

4x^2+56x-204=0

a = 4; b = 56; c = -204;
Δ = b2-4ac
Δ = 562-4·4·(-204)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-80}{2*4}=\frac{-136}{8}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+80}{2*4}=\frac{24}{8}
=3
$