4k(k-8)=-32+4k

Solution for 4k(k-8)=-32+4k equation:

4k(k-8)=-32+4k

We move all terms to the left:

4k(k-8)-(-32+4k)=0

We add all the numbers together, and all the variables

4k(k-8)-(4k-32)=0

We multiply parentheses

4k^2-32k-(4k-32)=0

We get rid of parentheses

4k^2-32k-4k+32=0

We add all the numbers together, and all the variables

4k^2-36k+32=0

a = 4; b = -36; c = +32;
Δ = b2-4ac
Δ = -362-4·4·32
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{-(-36)-28}{2*4}=\frac{8}{8}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+28}{2*4}=\frac{64}{8}
=8
$