4k(9k+31)=-32

Solution for 4k(9k+31)=-32 equation:

4k(9k+31)=-32

We move all terms to the left:

4k(9k+31)-(-32)=0

We add all the numbers together, and all the variables

4k(9k+31)+32=0

We multiply parentheses

36k^2+124k+32=0

a = 36; b = 124; c = +32;
Δ = b2-4ac
Δ = 1242-4·36·32
Δ = 10768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10768}=\sqrt{16*673}=\sqrt{16}*\sqrt{673}=4\sqrt{673}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-4\sqrt{673}}{2*36}=\frac{-124-4\sqrt{673}}{72}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+4\sqrt{673}}{2*36}=\frac{-124+4\sqrt{673}}{72}
$