1/3t=t+-154

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

1/3t=t+-154

We move all terms to the left:

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


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3t-t+154=0

We multiply all the terms by the denominator


-t*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 = 213456
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:

$\sqrt{\Delta}=\sqrt{213456}=\sqrt{16*13341}=\sqrt{16}*\sqrt{13341}=4\sqrt{13341}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-4\sqrt{13341}}{2*-3}=\frac{-462-4\sqrt{13341}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+4\sqrt{13341}}{2*-3}=\frac{-462+4\sqrt{13341}}{-6}
$