(3x-2)(3x-2)-4=9x-6

Solution for (3x-2)(3x-2)-4=9x-6 equation:

(3x-2)(3x-2)-4=9x-6

We move all terms to the left:

(3x-2)(3x-2)-4-(9x-6)=0

We get rid of parentheses

(3x-2)(3x-2)-9x+6-4=0

We multiply parentheses ..

(+9x^2-6x-6x+4)-9x+6-4=0

We add all the numbers together, and all the variables

(+9x^2-6x-6x+4)-9x+2=0

We get rid of parentheses

9x^2-6x-6x-9x+4+2=0

We add all the numbers together, and all the variables

9x^2-21x+6=0

a = 9; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·9·6
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*9}=\frac{6}{18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*9}=\frac{36}{18}
=2
$