-3(k-8)(-k+5)=23

Solution for -3(k-8)(-k+5)=23 equation:

-3(k-8)(-k+5)=23

We move all terms to the left:

-3(k-8)(-k+5)-(23)=0

We add all the numbers together, and all the variables

-3(k-8)(-1k+5)-23=0

We multiply parentheses ..

-3(-1k^2+5k+8k-40)-23=0

We multiply parentheses

3k^2-15k-24k+120-23=0

We add all the numbers together, and all the variables

3k^2-39k+97=0

a = 3; b = -39; c = +97;
Δ = b2-4ac
Δ = -392-4·3·97
Δ = 357
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{357}}{2*3}=\frac{39-\sqrt{357}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{357}}{2*3}=\frac{39+\sqrt{357}}{6}
$