2t=9+5/t

Solution for 2t=9+5/t equation:

2t=9+5/t

We move all terms to the left:

2t-(9+5/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-(5/t+9)=0

We get rid of parentheses

2t-5/t-9=0

We multiply all the terms by the denominator


2t*t-9*t-5=0

We add all the numbers together, and all the variables

-9t+2t*t-5=0

Wy multiply elements

2t^2-9t-5=0

a = 2; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·2·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*2}=\frac{-2}{4}
=-1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*2}=\frac{20}{4}
=5
$