t=4t+8t/t

Solution for t=4t+8t/t equation:

t=4t+8t/t

We move all terms to the left:

t-(4t+8t/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

t-(+4t+8t/t)=0

We get rid of parentheses

t-4t-8t/t=0

We multiply all the terms by the denominator


t*t-4t*t-8t=0

We add all the numbers together, and all the variables

-8t+t*t-4t*t=0

Wy multiply elements

t^2-4t^2-8t=0

We add all the numbers together, and all the variables

-3t^2-8t=0

a = -3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-3)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-3}=\frac{0}{-6}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-3}=\frac{16}{-6}
=-2+2/3
$