0=16t-30-4/t

Solution for 0=16t-30-4/t equation:

0=16t-30-4/t

We move all terms to the left:

0-(16t-30-4/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-4/t-30)+0=0

We add all the numbers together, and all the variables

-(16t-4/t-30)=0

We get rid of parentheses

-16t+4/t+30=0

We multiply all the terms by the denominator


-16t*t+30*t+4=0

We add all the numbers together, and all the variables

30t-16t*t+4=0

Wy multiply elements

-16t^2+30t+4=0

a = -16; b = 30; c = +4;
Δ = b2-4ac
Δ = 302-4·(-16)·4
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-34}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+34}{2*-16}=\frac{4}{-32}
=-1/8
$