2/3t-1=1/2t

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

2/3t-1=1/2t

We move all terms to the left:

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


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 2t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4t/6t^2+(-3t)/6t^2-1=0

We multiply all the terms by the denominator


4t+(-3t)-1*6t^2=0

Wy multiply elements

-6t^2+4t+(-3t)=0

We get rid of parentheses

-6t^2+4t-3t=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
$