16-2t=2/3t+9

Solution for 16-2t=2/3t+9 equation:

16-2t=2/3t+9

We move all terms to the left:

16-2t-(2/3t+9)=0


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

t∈R


We get rid of parentheses

-2t-2/3t-9+16=0

We multiply all the terms by the denominator


-2t*3t-9*3t+16*3t-2=0

Wy multiply elements

-6t^2-27t+48t-2=0

We add all the numbers together, and all the variables

-6t^2+21t-2=0

a = -6; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-6)·(-2)
Δ = 393
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{393}}{2*-6}=\frac{-21-\sqrt{393}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{393}}{2*-6}=\frac{-21+\sqrt{393}}{-12}
$