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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-6x-2x+4)-7=0

We get rid of parentheses

3x^2-6x-2x+4-7=0

We add all the numbers together, and all the variables

3x^2-8x-3=0

a = 3; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·3·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*3}=\frac{18}{6}
=3
$