3k2+30k=-48

Solution for 3k2+30k=-48 equation:

3k^2+30k=-48

We move all terms to the left:

3k^2+30k-(-48)=0

We add all the numbers together, and all the variables

3k^2+30k+48=0

a = 3; b = 30; c = +48;
Δ = b2-4ac
Δ = 302-4·3·48
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*3}=\frac{-48}{6}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*3}=\frac{-12}{6}
=-2
$