(3x-2)(3x-2)=0.25

Solution for (3x-2)(3x-2)=0.25 equation:

(3x-2)(3x-2)=0.25

We move all terms to the left:

(3x-2)(3x-2)-(0.25)=0

We add all the numbers together, and all the variables

(3x-2)(3x-2)-0.25=0

We multiply parentheses ..

(+9x^2-6x-6x+4)-0.25=0

We get rid of parentheses

9x^2-6x-6x+4-0.25=0

We add all the numbers together, and all the variables

9x^2-12x+3.75=0

a = 9; b = -12; c = +3.75;
Δ = b2-4ac
Δ = -122-4·9·3.75
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-3}{2*9}=\frac{9}{18}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+3}{2*9}=\frac{15}{18}
=5/6
$