(11+2x)(6+2x)=30

Solution for (11+2x)(6+2x)=30 equation:

(11+2x)(6+2x)=30

We move all terms to the left:

(11+2x)(6+2x)-(30)=0

We add all the numbers together, and all the variables

(2x+11)(2x+6)-30=0

We multiply parentheses ..

(+4x^2+12x+22x+66)-30=0

We get rid of parentheses

4x^2+12x+22x+66-30=0

We add all the numbers together, and all the variables

4x^2+34x+36=0

a = 4; b = 34; c = +36;
Δ = b2-4ac
Δ = 342-4·4·36
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{145}}{2*4}=\frac{-34-2\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{145}}{2*4}=\frac{-34+2\sqrt{145}}{8}
$