1/2t+3/4t=3/8

Solution for 1/2t+3/4t=3/8 equation:

1/2t+3/4t=3/8

We move all terms to the left:

1/2t+3/4t-(3/8)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We add all the numbers together, and all the variables

1/2t+3/4t-(+3/8)=0

We get rid of parentheses

1/2t+3/4t-3/8=0

We calculate fractions


(-96t^2)/512t^2+256t/512t^2+384t/512t^2=0

We multiply all the terms by the denominator


(-96t^2)+256t+384t=0

We add all the numbers together, and all the variables

(-96t^2)+640t=0

We get rid of parentheses

-96t^2+640t=0

a = -96; b = 640; c = 0;
Δ = b2-4ac
Δ = 6402-4·(-96)·0
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-640}{2*-96}=\frac{-1280}{-192}
=6+2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+640}{2*-96}=\frac{0}{-192}
=0
$