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)=0


Domain of the equation: 3t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = 48; c = -2;
Δ = b2-4ac
Δ = 482-4·(-6)·(-2)
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{141}}{2*-6}=\frac{-48-4\sqrt{141}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{141}}{2*-6}=\frac{-48+4\sqrt{141}}{-12}
$