154-t=1/3t

Solution for 154-t=1/3t equation:

154-t=1/3t

We move all terms to the left:

154-t-(1/3t)=0


Domain of the equation: 3t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-t-(+1/3t)+154=0

We add all the numbers together, and all the variables

-1t-(+1/3t)+154=0

We get rid of parentheses

-1t-1/3t+154=0

We multiply all the terms by the denominator


-1t*3t+154*3t-1=0

Wy multiply elements

-3t^2+462t-1=0

a = -3; b = 462; c = -1;
Δ = b2-4ac
Δ = 4622-4·(-3)·(-1)
Δ = 213432
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:

$\sqrt{\Delta}=\sqrt{213432}=\sqrt{4*53358}=\sqrt{4}*\sqrt{53358}=2\sqrt{53358}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-2\sqrt{53358}}{2*-3}=\frac{-462-2\sqrt{53358}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+2\sqrt{53358}}{2*-3}=\frac{-462+2\sqrt{53358}}{-6}
$