6k^2+30k=-24

Solution for 6k^2+30k=-24 equation:

6k^2+30k=-24

We move all terms to the left:

6k^2+30k-(-24)=0

We add all the numbers together, and all the variables

6k^2+30k+24=0

a = 6; b = 30; c = +24;
Δ = b2-4ac
Δ = 302-4·6·24
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18}{2*6}=\frac{-48}{12}
=-4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*6}=\frac{-12}{12}
=-1
$