(1/2)x-2=2(-x+1)

Solution for (1/2)x-2=2(-x+1) equation:

(1/2)x-2=2(-x+1)

We move all terms to the left:

(1/2)x-2-(2(-x+1))=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x-(2(-1x+1))-2=0

We multiply parentheses

x^2-(2(-1x+1))-2=0


We calculate terms in parentheses: -(2(-1x+1)), so:

2(-1x+1)

We multiply parentheses

-2x+2

Back to the equation:

-(-2x+2)


We get rid of parentheses

x^2+2x-2-2=0

We add all the numbers together, and all the variables

x^2+2x-4=0

a = 1; b = 2; c = -4;
Δ = b2-4ac
Δ = 22-4·1·(-4)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*1}=\frac{-2-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*1}=\frac{-2+2\sqrt{5}}{2}
$