1/2t-1/4t=5/8

Solution for 1/2t-1/4t=5/8 equation:

1/2t-1/4t=5/8

We move all terms to the left:

1/2t-1/4t-(5/8)=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-1/4t-(+5/8)=0

We get rid of parentheses

1/2t-1/4t-5/8=0

We calculate fractions


(-160t^2)/512t^2+256t/512t^2+(-128t)/512t^2=0

We multiply all the terms by the denominator


(-160t^2)+256t+(-128t)=0

We get rid of parentheses

-160t^2+256t-128t=0

We add all the numbers together, and all the variables

-160t^2+128t=0

a = -160; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·(-160)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*-160}=\frac{-256}{-320}
=4/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*-160}=\frac{0}{-320}
=0
$