1/t-1/2t=1

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

1/t-1/2t=1

We move all terms to the left:

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


Domain of the equation: t!=0

t∈R



Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We calculate fractions


2t/2t^2+(-t)/2t^2-1=0

We add all the numbers together, and all the variables

2t/2t^2+(-1t)/2t^2-1=0

We multiply all the terms by the denominator


2t+(-1t)-1*2t^2=0

Wy multiply elements

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

We get rid of parentheses

-2t^2+2t-1t=0

We add all the numbers together, and all the variables

-2t^2+t=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:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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