(1/6)t+5/6=3

Solution for (1/6)t+5/6=3 equation:

(1/6)t+5/6=3

We move all terms to the left:

(1/6)t+5/6-(3)=0


Domain of the equation: 6)t!=0

t!=0/1

t!=0

t∈R


determiningTheFunctionDomain
(1/6)t-3+5/6=0

We add all the numbers together, and all the variables

(+1/6)t-3+5/6=0

We multiply parentheses

t^2-3+5/6=0

We multiply all the terms by the denominator


t^2*6+5-3*6=0

We add all the numbers together, and all the variables

t^2*6-13=0

Wy multiply elements

6t^2-13=0

a = 6; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·6·(-13)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*6}=\frac{0-2\sqrt{78}}{12}
=-\frac{2\sqrt{78}}{12}
=-\frac{\sqrt{78}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*6}=\frac{0+2\sqrt{78}}{12}
=\frac{2\sqrt{78}}{12}
=\frac{\sqrt{78}}{6}
$