(6k+1)(k+7)=0

Solution for (6k+1)(k+7)=0 equation:

(6k+1)(k+7)=0

We multiply parentheses ..

(+6k^2+42k+k+7)=0

We get rid of parentheses

6k^2+42k+k+7=0

We add all the numbers together, and all the variables

6k^2+43k+7=0

a = 6; b = 43; c = +7;
Δ = b2-4ac
Δ = 432-4·6·7
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-41}{2*6}=\frac{-84}{12}
=-7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+41}{2*6}=\frac{-2}{12}
=-1/6
$