16-2t=3/2t*9

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

16-2t=3/2t*9

We move all terms to the left:

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


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

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-36t^2*9+288t*9-3=0

Wy multiply elements

-324t^2+2592t-3=0

a = -324; b = 2592; c = -3;
Δ = b2-4ac
Δ = 25922-4·(-324)·(-3)
Δ = 6714576
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:

$\sqrt{\Delta}=\sqrt{6714576}=\sqrt{1296*5181}=\sqrt{1296}*\sqrt{5181}=36\sqrt{5181}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2592)-36\sqrt{5181}}{2*-324}=\frac{-2592-36\sqrt{5181}}{-648}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2592)+36\sqrt{5181}}{2*-324}=\frac{-2592+36\sqrt{5181}}{-648}
$