4t/t-25=1/5-t

Solution for 4t/t-25=1/5-t equation:

4t/t-25=1/5-t

We move all terms to the left:

4t/t-25-(1/5-t)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 5-t)!=0

We move all terms containing t to the left, all other terms to the right

-t)!=-5

t!=-5/1

t!=-5

t∈R


We add all the numbers together, and all the variables

4t/t-(-1t+1/5)-25=0

We get rid of parentheses

4t/t+1t-25-1/5=0

We calculate fractions


1t+20t/5t+(-t)/5t-25=0

We add all the numbers together, and all the variables

1t+20t/5t+(-1t)/5t-25=0

We add all the numbers together, and all the variables

t+20t/5t+(-1t)/5t-25=0

We multiply all the terms by the denominator


t*5t+20t+(-1t)-25*5t=0

We add all the numbers together, and all the variables

20t+t*5t+(-1t)-25*5t=0

Wy multiply elements

5t^2+20t+(-1t)-125t=0

We get rid of parentheses

5t^2+20t-1t-125t=0

We add all the numbers together, and all the variables

5t^2-106t=0

a = 5; b = -106; c = 0;
Δ = b2-4ac
Δ = -1062-4·5·0
Δ = 11236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11236}=106$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-106}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+106}{2*5}=\frac{212}{10}
=21+1/5
$