3(t-1)=9/t

Solution for 3(t-1)=9/t equation:

3(t-1)=9/t

We move all terms to the left:

3(t-1)-(9/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

3(t-1)-(+9/t)=0

We multiply parentheses

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

We get rid of parentheses

3t-9/t-3=0

We multiply all the terms by the denominator


3t*t-3*t-9=0

We add all the numbers together, and all the variables

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

Wy multiply elements

3t^2-3t-9=0

a = 3; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·3·(-9)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{13}}{2*3}=\frac{3-3\sqrt{13}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{13}}{2*3}=\frac{3+3\sqrt{13}}{6}
$