3/4t-5/9=2/3t

Solution for 3/4t-5/9=2/3t equation:

3/4t-5/9=2/3t

We move all terms to the left:

3/4t-5/9-(2/3t)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 3t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

3/4t-(+2/3t)-5/9=0

We get rid of parentheses

3/4t-2/3t-5/9=0

We calculate fractions


(-180t^2)/972t^2+729t/972t^2+(-648t)/972t^2=0

We multiply all the terms by the denominator


(-180t^2)+729t+(-648t)=0

We get rid of parentheses

-180t^2+729t-648t=0

We add all the numbers together, and all the variables

-180t^2+81t=0

a = -180; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-180)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-180}=\frac{-162}{-360}
=9/20
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-180}=\frac{0}{-360}
=0
$