2t=1/3t+7

Solution for 2t=1/3t+7 equation:

2t=1/3t+7

We move all terms to the left:

2t-(1/3t+7)=0


Domain of the equation: 3t+7)!=0

t∈R


We get rid of parentheses

2t-1/3t-7=0

We multiply all the terms by the denominator


2t*3t-7*3t-1=0

Wy multiply elements

6t^2-21t-1=0

a = 6; b = -21; c = -1;
Δ = b2-4ac
Δ = -212-4·6·(-1)
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{465}}{2*6}=\frac{21-\sqrt{465}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*6}=\frac{21+\sqrt{465}}{12}
$