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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

42x^2+36x-6=0

a = 42; b = 36; c = -6;
Δ = b2-4ac
Δ = 362-4·42·(-6)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-48}{2*42}=\frac{-84}{84}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+48}{2*42}=\frac{12}{84}
=1/7
$