6(8k+5)(k+7)=0

Solution for 6(8k+5)(k+7)=0 equation:

6(8k+5)(k+7)=0

We multiply parentheses ..

6(+8k^2+56k+5k+35)=0

We multiply parentheses

48k^2+336k+30k+210=0

We add all the numbers together, and all the variables

48k^2+366k+210=0

a = 48; b = 366; c = +210;
Δ = b2-4ac
Δ = 3662-4·48·210
Δ = 93636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{93636}=306$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(366)-306}{2*48}=\frac{-672}{96}
=-7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(366)+306}{2*48}=\frac{-60}{96}
=-5/8
$