6-2t=2/3t+9

Solution for 6-2t=2/3t+9 equation:

6-2t=2/3t+9

We move all terms to the left:

6-2t-(2/3t+9)=0


Domain of the equation: 3t+9)!=0

t∈R


We get rid of parentheses

-2t-2/3t-9+6=0

We multiply all the terms by the denominator


-2t*3t-9*3t+6*3t-2=0

Wy multiply elements

-6t^2-27t+18t-2=0

We add all the numbers together, and all the variables

-6t^2-9t-2=0

a = -6; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·(-6)·(-2)
Δ = 33
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{-(-9)-\sqrt{33}}{2*-6}=\frac{9-\sqrt{33}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*-6}=\frac{9+\sqrt{33}}{-12}
$