6k(k+4)=k-20

Solution for 6k(k+4)=k-20 equation:

6k(k+4)=k-20

We move all terms to the left:

6k(k+4)-(k-20)=0

We multiply parentheses

6k^2+24k-(k-20)=0

We get rid of parentheses

6k^2+24k-k+20=0

We add all the numbers together, and all the variables

6k^2+23k+20=0

a = 6; b = 23; c = +20;
Δ = b2-4ac
Δ = 232-4·6·20
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*6}=\frac{-30}{12}
=-2+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*6}=\frac{-16}{12}
=-1+1/3
$