(x+11)(2x+1)=(4x+5)(x+11)

Solution for (x+11)(2x+1)=(4x+5)(x+11) equation:

(x+11)(2x+1)=(4x+5)(x+11)

We move all terms to the left:

(x+11)(2x+1)-((4x+5)(x+11))=0

We multiply parentheses ..

(+2x^2+x+22x+11)-((4x+5)(x+11))=0


We calculate terms in parentheses: -((4x+5)(x+11)), so:

(4x+5)(x+11)

We multiply parentheses ..

(+4x^2+44x+5x+55)

We get rid of parentheses

4x^2+44x+5x+55

We add all the numbers together, and all the variables

4x^2+49x+55

Back to the equation:

-(4x^2+49x+55)


We get rid of parentheses

2x^2-4x^2+x+22x-49x+11-55=0

We add all the numbers together, and all the variables

-2x^2-26x-44=0

a = -2; b = -26; c = -44;
Δ = b2-4ac
Δ = -262-4·(-2)·(-44)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-18}{2*-2}=\frac{8}{-4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+18}{2*-2}=\frac{44}{-4}
=-11
$