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

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

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

We move all terms to the left:

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


Domain of the equation: t!=0

t∈R



Domain of the equation: 2t+9)!=0

t∈R


We get rid of parentheses

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

We calculate fractions


(-4t)/2t^2+(-3t)/2t^2-9+16=0

We add all the numbers together, and all the variables

(-4t)/2t^2+(-3t)/2t^2+7=0

We multiply all the terms by the denominator


(-4t)+(-3t)+7*2t^2=0

Wy multiply elements

14t^2+(-4t)+(-3t)=0

We get rid of parentheses

14t^2-4t-3t=0

We add all the numbers together, and all the variables

14t^2-7t=0

a = 14; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·14·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*14}=\frac{0}{28}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*14}=\frac{14}{28}
=1/2
$