4k(k-8)=-38+4k

Solution for 4k(k-8)=-38+4k equation:

4k(k-8)=-38+4k

We move all terms to the left:

4k(k-8)-(-38+4k)=0

We add all the numbers together, and all the variables

4k(k-8)-(4k-38)=0

We multiply parentheses

4k^2-32k-(4k-38)=0

We get rid of parentheses

4k^2-32k-4k+38=0

We add all the numbers together, and all the variables

4k^2-36k+38=0

a = 4; b = -36; c = +38;
Δ = b2-4ac
Δ = -362-4·4·38
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{43}}{2*4}=\frac{36-4\sqrt{43}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{43}}{2*4}=\frac{36+4\sqrt{43}}{8}
$