1/2t-3/4=3/5t

Solution for 1/2t-3/4=3/5t equation:

1/2t-3/4=3/5t

We move all terms to the left:

1/2t-3/4-(3/5t)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 5t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

1/2t-(+3/5t)-3/4=0

We get rid of parentheses

1/2t-3/5t-3/4=0

We calculate fractions


(-150t^2)/160t^2+80t/160t^2+(-96t)/160t^2=0

We multiply all the terms by the denominator


(-150t^2)+80t+(-96t)=0

We get rid of parentheses

-150t^2+80t-96t=0

We add all the numbers together, and all the variables

-150t^2-16t=0

a = -150; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-150)·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*-150}=\frac{0}{-300}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-150}=\frac{32}{-300}
=-8/75
$