-3k(1+9k)-7(-12k+1)=1+10k-11-6k

Solution for -3k(1+9k)-7(-12k+1)=1+10k-11-6k equation:

-3k(1+9k)-7(-12k+1)=1+10k-11-6k

We move all terms to the left:

-3k(1+9k)-7(-12k+1)-(1+10k-11-6k)=0

We add all the numbers together, and all the variables

-3k(9k+1)-7(-12k+1)-(4k-10)=0

We multiply parentheses

-27k^2-3k+84k-(4k-10)-7=0

We get rid of parentheses

-27k^2-3k+84k-4k+10-7=0

We add all the numbers together, and all the variables

-27k^2+77k+3=0

a = -27; b = 77; c = +3;
Δ = b2-4ac
Δ = 772-4·(-27)·3
Δ = 6253
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:

$\sqrt{\Delta}=\sqrt{6253}=\sqrt{169*37}=\sqrt{169}*\sqrt{37}=13\sqrt{37}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-13\sqrt{37}}{2*-27}=\frac{-77-13\sqrt{37}}{-54}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+13\sqrt{37}}{2*-27}=\frac{-77+13\sqrt{37}}{-54}
$