16-2t=3/5t+9

Solution for 16-2t=3/5t+9 equation:

16-2t=3/5t+9

We move all terms to the left:

16-2t-(3/5t+9)=0


Domain of the equation: 5t+9)!=0

t∈R


We get rid of parentheses

-2t-3/5t-9+16=0

We multiply all the terms by the denominator


-2t*5t-9*5t+16*5t-3=0

Wy multiply elements

-10t^2-45t+80t-3=0

We add all the numbers together, and all the variables

-10t^2+35t-3=0

a = -10; b = 35; c = -3;
Δ = b2-4ac
Δ = 352-4·(-10)·(-3)
Δ = 1105
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{-(35)-\sqrt{1105}}{2*-10}=\frac{-35-\sqrt{1105}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1105}}{2*-10}=\frac{-35+\sqrt{1105}}{-20}
$