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

Solution for (5k-3)(3k+8)=0 equation:

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

We multiply parentheses ..

(+15k^2+40k-9k-24)=0

We get rid of parentheses

15k^2+40k-9k-24=0

We add all the numbers together, and all the variables

15k^2+31k-24=0

a = 15; b = 31; c = -24;
Δ = b2-4ac
Δ = 312-4·15·(-24)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-49}{2*15}=\frac{-80}{30}
=-2+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+49}{2*15}=\frac{18}{30}
=3/5
$