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

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

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

We multiply parentheses ..

(+42k^2+6k-49k-7)=0

We get rid of parentheses

42k^2+6k-49k-7=0

We add all the numbers together, and all the variables

42k^2-43k-7=0

a = 42; b = -43; c = -7;
Δ = b2-4ac
Δ = -432-4·42·(-7)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-55}{2*42}=\frac{-12}{84}
=-1/7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+55}{2*42}=\frac{98}{84}
=1+1/6
$