(5k+6)(3k+8)=0

Solution for (5k+6)(3k+8)=0 equation:

(5k+6)(3k+8)=0

We multiply parentheses ..

(+15k^2+40k+18k+48)=0

We get rid of parentheses

15k^2+40k+18k+48=0

We add all the numbers together, and all the variables

15k^2+58k+48=0

a = 15; b = 58; c = +48;
Δ = b2-4ac
Δ = 582-4·15·48
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-22}{2*15}=\frac{-80}{30}
=-2+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+22}{2*15}=\frac{-36}{30}
=-1+1/5
$