2t/t+1+5/2t=2

Solution for 2t/t+1+5/2t=2 equation:

2t/t+1+5/2t=2

We move all terms to the left:

2t/t+1+5/2t-(2)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

2t/t+5/2t-1=0

We calculate fractions


4t^2/2t^2+5t/2t^2-1=0

We multiply all the terms by the denominator


4t^2+5t-1*2t^2=0

Wy multiply elements

4t^2-2t^2+5t=0

We add all the numbers together, and all the variables

2t^2+5t=0

a = 2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*2}=\frac{-10}{4}
=-2+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*2}=\frac{0}{4}
=0
$