(2x-2)(-3x+7)=0

Solution for (2x-2)(-3x+7)=0 equation:

(2x-2)(-3x+7)=0

We multiply parentheses ..

(-6x^2+14x+6x-14)=0

We get rid of parentheses

-6x^2+14x+6x-14=0

We add all the numbers together, and all the variables

-6x^2+20x-14=0

a = -6; b = 20; c = -14;
Δ = b2-4ac
Δ = 202-4·(-6)·(-14)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8}{2*-6}=\frac{-28}{-12}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8}{2*-6}=\frac{-12}{-12}
=1
$