T=-16t+55+5/t

Solution for T=-16t+55+5/t equation:

=-16T+55+5/T

We move all terms to the left:

-(-16T+55+5/T)=0


Domain of the equation: T)!=0

T!=0/1

T!=0

T∈R


We add all the numbers together, and all the variables

-(-16T+5/T+55)=0

We get rid of parentheses

16T-5/T-55=0

We multiply all the terms by the denominator


16T*T-55*T-5=0

We add all the numbers together, and all the variables

-55T+16T*T-5=0

Wy multiply elements

16T^2-55T-5=0

a = 16; b = -55; c = -5;
Δ = b2-4ac
Δ = -552-4·16·(-5)
Δ = 3345
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{-(-55)-\sqrt{3345}}{2*16}=\frac{55-\sqrt{3345}}{32}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3345}}{2*16}=\frac{55+\sqrt{3345}}{32}
$