t=13/12t

Solution for t=13/12t equation:

t=13/12t

We move all terms to the left:

t-(13/12t)=0


Domain of the equation: 12t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

t-(+13/12t)=0

We get rid of parentheses

t-13/12t=0

We multiply all the terms by the denominator


t*12t-13=0

Wy multiply elements

12t^2-13=0

a = 12; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·12·(-13)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*12}=\frac{0-4\sqrt{39}}{24}
=-\frac{4\sqrt{39}}{24}
=-\frac{\sqrt{39}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*12}=\frac{0+4\sqrt{39}}{24}
=\frac{4\sqrt{39}}{24}
=\frac{\sqrt{39}}{6}
$