3/2+5/4t=9/8t

Solution for 3/2+5/4t=9/8t equation:

3/2+5/4t=9/8t

We move all terms to the left:

3/2+5/4t-(9/8t)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 8t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

5/4t-(+9/8t)+3/2=0

We get rid of parentheses

5/4t-9/8t+3/2=0

We calculate fractions


768t^2/128t^2+160t/128t^2+(-144t)/128t^2=0

We multiply all the terms by the denominator


768t^2+160t+(-144t)=0

We get rid of parentheses

768t^2+160t-144t=0

We add all the numbers together, and all the variables

768t^2+16t=0

a = 768; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·768·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*768}=\frac{-32}{1536}
=-1/48
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*768}=\frac{0}{1536}
=0
$