1/5t-0.4+2/5t=0.6-1/10t

Solution for 1/5t-0.4+2/5t=0.6-1/10t equation:

1/5t-0.4+2/5t=0.6-1/10t

We move all terms to the left:

1/5t-0.4+2/5t-(0.6-1/10t)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 10t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

1/5t+2/5t-(-1/10t+0.6)-0.4=0

We get rid of parentheses

1/5t+2/5t+1/10t-0.6-0.4=0

We calculate fractions


(20t+1)/50t^2+5t/50t^2-0.6-0.4=0

We add all the numbers together, and all the variables

(20t+1)/50t^2+5t/50t^2-1=0

We multiply all the terms by the denominator


(20t+1)+5t-1*50t^2=0

We add all the numbers together, and all the variables

5t+(20t+1)-1*50t^2=0

Wy multiply elements

-50t^2+5t+(20t+1)=0

We get rid of parentheses

-50t^2+5t+20t+1=0

We add all the numbers together, and all the variables

-50t^2+25t+1=0

a = -50; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·(-50)·1
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{33}}{2*-50}=\frac{-25-5\sqrt{33}}{-100}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{33}}{2*-50}=\frac{-25+5\sqrt{33}}{-100}
$