3(3k+24)(3k-7)=0

Solution for 3(3k+24)(3k-7)=0 equation:

3(3k+24)(3k-7)=0

We multiply parentheses ..

3(+9k^2-21k+72k-168)=0

We multiply parentheses

27k^2-63k+216k-504=0

We add all the numbers together, and all the variables

27k^2+153k-504=0

a = 27; b = 153; c = -504;
Δ = b2-4ac
Δ = 1532-4·27·(-504)
Δ = 77841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77841}=279$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(153)-279}{2*27}=\frac{-432}{54}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(153)+279}{2*27}=\frac{126}{54}
=2+1/3
$