-6k(k-2)=-6(1+4k)

Solution for -6k(k-2)=-6(1+4k) equation:

-6k(k-2)=-6(1+4k)

We move all terms to the left:

-6k(k-2)-(-6(1+4k))=0

We add all the numbers together, and all the variables

-6k(k-2)-(-6(4k+1))=0

We multiply parentheses

-6k^2+12k-(-6(4k+1))=0


We calculate terms in parentheses: -(-6(4k+1)), so:

-6(4k+1)

We multiply parentheses

-24k-6

Back to the equation:

-(-24k-6)


We get rid of parentheses

-6k^2+12k+24k+6=0

We add all the numbers together, and all the variables

-6k^2+36k+6=0

a = -6; b = 36; c = +6;
Δ = b2-4ac
Δ = 362-4·(-6)·6
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{10}}{2*-6}=\frac{-36-12\sqrt{10}}{-12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{10}}{2*-6}=\frac{-36+12\sqrt{10}}{-12}
$