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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12x^2+50x-42=0

a = -12; b = 50; c = -42;
Δ = b2-4ac
Δ = 502-4·(-12)·(-42)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-22}{2*-12}=\frac{-72}{-24}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+22}{2*-12}=\frac{-28}{-24}
=1+1/6
$