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

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

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

We multiply parentheses ..

(+12x^2+36x-14x-42)=0

We get rid of parentheses

12x^2+36x-14x-42=0

We add all the numbers together, and all the variables

12x^2+22x-42=0

a = 12; b = 22; c = -42;
Δ = b2-4ac
Δ = 222-4·12·(-42)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-50}{2*12}=\frac{-72}{24}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+50}{2*12}=\frac{28}{24}
=1+1/6
$