8k^2=-40-48k

Solution for 8k^2=-40-48k equation:

8k^2=-40-48k

We move all terms to the left:

8k^2-(-40-48k)=0

We add all the numbers together, and all the variables

8k^2-(-48k-40)=0

We get rid of parentheses

8k^2+48k+40=0

a = 8; b = 48; c = +40;
Δ = b2-4ac
Δ = 482-4·8·40
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-32}{2*8}=\frac{-80}{16}
=-5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+32}{2*8}=\frac{-16}{16}
=-1
$