12(2k+11)=12(2k+12)k=

Solution for 12(2k+11)=12(2k+12)k= equation:

12(2k+11)=12(2k+12)k=

We move all terms to the left:

12(2k+11)-(12(2k+12)k)=0

We multiply parentheses

24k-(12(2k+12)k)+132=0


We calculate terms in parentheses: -(12(2k+12)k), so:

12(2k+12)k

We multiply parentheses

24k^2+144k

Back to the equation:

-(24k^2+144k)


We get rid of parentheses

-24k^2+24k-144k+132=0

We add all the numbers together, and all the variables

-24k^2-120k+132=0

a = -24; b = -120; c = +132;
Δ = b2-4ac
Δ = -1202-4·(-24)·132
Δ = 27072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27072}=\sqrt{576*47}=\sqrt{576}*\sqrt{47}=24\sqrt{47}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{47}}{2*-24}=\frac{120-24\sqrt{47}}{-48}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{47}}{2*-24}=\frac{120+24\sqrt{47}}{-48}
$