-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 multiply parentheses ..

-3(+k^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+9k+97=0

a = -3; b = 9; c = +97;
Δ = b2-4ac
Δ = 92-4·(-3)·97
Δ = 1245
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{-(9)-\sqrt{1245}}{2*-3}=\frac{-9-\sqrt{1245}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{1245}}{2*-3}=\frac{-9+\sqrt{1245}}{-6}
$