(3k+8)(2k-5)=0

Solution for (3k+8)(2k-5)=0 equation:

(3k+8)(2k-5)=0

We multiply parentheses ..

(+6k^2-15k+16k-40)=0

We get rid of parentheses

6k^2-15k+16k-40=0

We add all the numbers together, and all the variables

6k^2+k-40=0

a = 6; b = 1; c = -40;
Δ = b2-4ac
Δ = 12-4·6·(-40)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*6}=\frac{-32}{12}
=-2+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*6}=\frac{30}{12}
=2+1/2
$