16-2t=4/6t+9

Solution for 16-2t=4/6t+9 equation:

16-2t=4/6t+9

We move all terms to the left:

16-2t-(4/6t+9)=0


Domain of the equation: 6t+9)!=0

t∈R


We get rid of parentheses

-2t-4/6t-9+16=0

We multiply all the terms by the denominator


-2t*6t-9*6t+16*6t-4=0

Wy multiply elements

-12t^2-54t+96t-4=0

We add all the numbers together, and all the variables

-12t^2+42t-4=0

a = -12; b = 42; c = -4;
Δ = b2-4ac
Δ = 422-4·(-12)·(-4)
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{393}}{2*-12}=\frac{-42-2\sqrt{393}}{-24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{393}}{2*-12}=\frac{-42+2\sqrt{393}}{-24}
$