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

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

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

We move all terms to the left:

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


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 5t+1t)!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


-t+()/10t+5t/10t-1=0

We add all the numbers together, and all the variables

-1t+()/10t+5t/10t-1=0

We multiply all the terms by the denominator


-1t*10t+5t-1*10t+()=0

We add all the numbers together, and all the variables

5t-1t*10t-1*10t=0

Wy multiply elements

-10t^2+5t-10t=0

We add all the numbers together, and all the variables

-10t^2-5t=0

a = -10; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-10)·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*-10}=\frac{0}{-20}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-10}=\frac{10}{-20}
=-1/2
$