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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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