4k^2=-48-28k

Solution for 4k^2=-48-28k equation:

4k^2=-48-28k

We move all terms to the left:

4k^2-(-48-28k)=0

We add all the numbers together, and all the variables

4k^2-(-28k-48)=0

We get rid of parentheses

4k^2+28k+48=0

a = 4; b = 28; c = +48;
Δ = b2-4ac
Δ = 282-4·4·48
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4}{2*4}=\frac{-32}{8}
=-4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4}{2*4}=\frac{-24}{8}
=-3
$