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

Solution for (3+2t)-(8+1)=2/t equation:

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

We move all terms to the left:

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


Domain of the equation: t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(2t+3)-(+2/t)-9=0

We get rid of parentheses

2t-2/t+3-9=0

We multiply all the terms by the denominator


2t*t+3*t-9*t-2=0

We add all the numbers together, and all the variables

-6t+2t*t-2=0

Wy multiply elements

2t^2-6t-2=0

a = 2; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·2·(-2)
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*2}=\frac{6-2\sqrt{13}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*2}=\frac{6+2\sqrt{13}}{4}
$