k(8+3+k)=8k

Solution for k(8+3+k)=8k equation:

k(8+3+k)=8k

We move all terms to the left:

k(8+3+k)-(8k)=0

We add all the numbers together, and all the variables

k(k+11)-8k=0

We add all the numbers together, and all the variables

-8k+k(k+11)=0

We multiply parentheses

k^2-8k+11k=0

We add all the numbers together, and all the variables

k^2+3k=0

a = 1; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·1·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*1}=\frac{-6}{2}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*1}=\frac{0}{2}
=0
$