(6k-1)(3k+8)=0

Solution for (6k-1)(3k+8)=0 equation:

(6k-1)(3k+8)=0

We multiply parentheses ..

(+18k^2+48k-3k-8)=0

We get rid of parentheses

18k^2+48k-3k-8=0

We add all the numbers together, and all the variables

18k^2+45k-8=0

a = 18; b = 45; c = -8;
Δ = b2-4ac
Δ = 452-4·18·(-8)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-51}{2*18}=\frac{-96}{36}
=-2+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+51}{2*18}=\frac{6}{36}
=1/6
$