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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: +(x(x-2)), so:

x(x-2)

We multiply parentheses

x^2-2x

Back to the equation:

+(x^2-2x)


We add all the numbers together, and all the variables

(x^2-2x)-5=0

We get rid of parentheses

x^2-2x-5=0

a = 1; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·1·(-5)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*1}=\frac{2-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*1}=\frac{2+2\sqrt{6}}{2}
$