5k^2=-12-32k

Solution for 5k^2=-12-32k equation:

5k^2=-12-32k

We move all terms to the left:

5k^2-(-12-32k)=0

We add all the numbers together, and all the variables

5k^2-(-32k-12)=0

We get rid of parentheses

5k^2+32k+12=0

a = 5; b = 32; c = +12;
Δ = b2-4ac
Δ = 322-4·5·12
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-28}{2*5}=\frac{-60}{10}
=-6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+28}{2*5}=\frac{-4}{10}
=-2/5
$