(6x-6)(7x+2)=0

Solution for (6x-6)(7x+2)=0 equation:

(6x-6)(7x+2)=0

We multiply parentheses ..

(+42x^2+12x-42x-12)=0

We get rid of parentheses

42x^2+12x-42x-12=0

We add all the numbers together, and all the variables

42x^2-30x-12=0

a = 42; b = -30; c = -12;
Δ = b2-4ac
Δ = -302-4·42·(-12)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-54}{2*42}=\frac{-24}{84}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+54}{2*42}=\frac{84}{84}
=1
$