(x-2)(x-2)=2.5

Solution for (x-2)(x-2)=2.5 equation:

(x-2)(x-2)=2.5

We move all terms to the left:

(x-2)(x-2)-(2.5)=0

We add all the numbers together, and all the variables

(x-2)(x-2)-2.5=0

We multiply parentheses ..

(+x^2-2x-2x+4)-2.5=0

We get rid of parentheses

x^2-2x-2x+4-2.5=0

We add all the numbers together, and all the variables

x^2-4x+1.5=0

a = 1; b = -4; c = +1.5;
Δ = b2-4ac
Δ = -42-4·1·1.5
Δ = 10
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{10}}{2*1}=\frac{4-\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{10}}{2*1}=\frac{4+\sqrt{10}}{2}
$