2/3t-2=3/4t+2

Solution for 2/3t-2=3/4t+2 equation:

2/3t-2=3/4t+2

We move all terms to the left:

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


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 4t+2)!=0

t∈R


We get rid of parentheses

2/3t-3/4t-2-2=0

We calculate fractions


8t/12t^2+(-9t)/12t^2-2-2=0

We add all the numbers together, and all the variables

8t/12t^2+(-9t)/12t^2-4=0

We multiply all the terms by the denominator


8t+(-9t)-4*12t^2=0

Wy multiply elements

-48t^2+8t+(-9t)=0

We get rid of parentheses

-48t^2+8t-9t=0

We add all the numbers together, and all the variables

-48t^2-1t=0

a = -48; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-48)·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*-48}=\frac{0}{-96}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-48}=\frac{2}{-96}
=-1/48
$