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

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

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

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4t+(-2t)+1*8t^2=0

Wy multiply elements

8t^2+4t+(-2t)=0

We get rid of parentheses

8t^2+4t-2t=0

We add all the numbers together, and all the variables

8t^2+2t=0

a = 8; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·8·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*8}=\frac{-4}{16}
=-1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*8}=\frac{0}{16}
=0
$