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

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

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

We multiply parentheses ..

(+42x^2-6x+7x-1)=0

We get rid of parentheses

42x^2-6x+7x-1=0

We add all the numbers together, and all the variables

42x^2+x-1=0

a = 42; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·42·(-1)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*42}=\frac{-14}{84}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*42}=\frac{12}{84}
=1/7
$