1/3t-3=1/6t

Solution for 1/3t-3=1/6t equation:

1/3t-3=1/6t

We move all terms to the left:

1/3t-3-(1/6t)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 6t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3t-1/6t-3=0

We calculate fractions


6t/18t^2+(-3t)/18t^2-3=0

We multiply all the terms by the denominator


6t+(-3t)-3*18t^2=0

Wy multiply elements

-54t^2+6t+(-3t)=0

We get rid of parentheses

-54t^2+6t-3t=0

We add all the numbers together, and all the variables

-54t^2+3t=0

a = -54; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-54)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-54}=\frac{-6}{-108}
=1/18
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-54}=\frac{0}{-108}
=0
$