X=t/2t-1

Solution for X=t/2t-1 equation:

X=X/2X-1

We move all terms to the left:

X-(X/2X-1)=0


Domain of the equation: 2X-1)!=0

X∈R


We get rid of parentheses

X-X/2X+1=0

We multiply all the terms by the denominator


X*2X-X+1*2X=0

We add all the numbers together, and all the variables

-1X+X*2X+1*2X=0

Wy multiply elements

2X^2-1X+2X=0

We add all the numbers together, and all the variables

2X^2+X=0

a = 2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*2}=\frac{-2}{4}
=-1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*2}=\frac{0}{4}
=0
$