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

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

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

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: t-2)!=0

t∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6t^2-1t=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{0}{12}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$