11=(2x+5)(6x-6)

Solution for 11=(2x+5)(6x-6) equation:

11=(2x+5)(6x-6)

We move all terms to the left:

11-((2x+5)(6x-6))=0

We multiply parentheses ..

-((+12x^2-12x+30x-30))+11=0


We calculate terms in parentheses: -((+12x^2-12x+30x-30)), so:

(+12x^2-12x+30x-30)

We get rid of parentheses

12x^2-12x+30x-30

We add all the numbers together, and all the variables

12x^2+18x-30

Back to the equation:

-(12x^2+18x-30)


We get rid of parentheses

-12x^2-18x+30+11=0

We add all the numbers together, and all the variables

-12x^2-18x+41=0

a = -12; b = -18; c = +41;
Δ = b2-4ac
Δ = -182-4·(-12)·41
Δ = 2292
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:

$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{573}}{2*-12}=\frac{18-2\sqrt{573}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{573}}{2*-12}=\frac{18+2\sqrt{573}}{-24}
$