1/2t-1/3t=-1

Solution for 1/2t-1/3t=-1 equation:

1/2t-1/3t=-1

We move all terms to the left:

1/2t-1/3t-(-1)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

1/2t-1/3t+1=0

We calculate fractions


3t/6t^2+(-2t)/6t^2+1=0

We multiply all the terms by the denominator


3t+(-2t)+1*6t^2=0

Wy multiply elements

6t^2+3t+(-2t)=0

We get rid of parentheses

6t^2+3t-2t=0

We add all the numbers together, and all the variables

6t^2+t=0

a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
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*6}=\frac{-2}{12}
=-1/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12}
=0
$