7/2t-1=1/4t+3

Solution for 7/2t-1=1/4t+3 equation:

7/2t-1=1/4t+3

We move all terms to the left:

7/2t-1-(1/4t+3)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t+3)!=0

t∈R


We get rid of parentheses

7/2t-1/4t-3-1=0

We calculate fractions


28t/8t^2+(-2t)/8t^2-3-1=0

We add all the numbers together, and all the variables

28t/8t^2+(-2t)/8t^2-4=0

We multiply all the terms by the denominator


28t+(-2t)-4*8t^2=0

Wy multiply elements

-32t^2+28t+(-2t)=0

We get rid of parentheses

-32t^2+28t-2t=0

We add all the numbers together, and all the variables

-32t^2+26t=0

a = -32; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-32)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-32}=\frac{-52}{-64}
=13/16
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-32}=\frac{0}{-64}
=0
$