(x-0.5)(x-0.5)=9

Solution for (x-0.5)(x-0.5)=9 equation:

(x-0.5)(x-0.5)=9

We move all terms to the left:

(x-0.5)(x-0.5)-(9)=0

We multiply parentheses ..

(+x^2-0.5x-0.5x+0.25)-9=0

We get rid of parentheses

x^2-0.5x-0.5x+0.25-9=0

We add all the numbers together, and all the variables

x^2-1x-8.75=0

a = 1; b = -1; c = -8.75;
Δ = b2-4ac
Δ = -12-4·1·(-8.75)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-6}{2*1}=\frac{-5}{2}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+6}{2*1}=\frac{7}{2}
=3+1/2
$