W=t-2/t+2

Solution for W=t-2/t+2 equation:

=W-2/W+2

We move all terms to the left:

-(W-2/W+2)=0


Domain of the equation: W+2)!=0

W∈R


We get rid of parentheses

-W+2/W-2=0

We multiply all the terms by the denominator


-W*W-2*W+2=0

We add all the numbers together, and all the variables

-2W-W*W+2=0

Wy multiply elements

-1W^2-2W+2=0

a = -1; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-1)·2
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*-1}=\frac{2-2\sqrt{3}}{-2}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*-1}=\frac{2+2\sqrt{3}}{-2}
$