7+3t=5+1/1t

Solution for 7+3t=5+1/1t equation:

7+3t=5+1/1t

We move all terms to the left:

7+3t-(5+1/1t)=0


Domain of the equation: 1t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

3t-(1/1t+5)+7=0

We get rid of parentheses

3t-1/1t-5+7=0

We multiply all the terms by the denominator


3t*1t-5*1t+7*1t-1=0

Wy multiply elements

3t^2-5t+7t-1=0

We add all the numbers together, and all the variables

3t^2+2t-1=0

a = 3; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·3·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4}{2*3}=\frac{-6}{6}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*3}=\frac{2}{6}
=1/3
$