(150/t)-170/(t+2)=16

Solution for (150/t)-170/(t+2)=16 equation:

(150/t)-170/(t+2)=16

We move all terms to the left:

(150/t)-170/(t+2)-(16)=0


Domain of the equation: t)!=0

t!=0/1

t!=0

t∈R



Domain of the equation: (t+2)!=0

We move all terms containing t to the left, all other terms to the right

t!=-2

t∈R


We add all the numbers together, and all the variables

(+150/t)-170/(t+2)-16=0

We get rid of parentheses

150/t-170/(t+2)-16=0

We calculate fractions


(150t+300)/(t^2+2t)+(-170t)/(t^2+2t)-16=0

We multiply all the terms by the denominator


(150t+300)+(-170t)-16*(t^2+2t)=0

We multiply parentheses

-16t^2+(150t+300)+(-170t)-32t=0

We get rid of parentheses

-16t^2+150t-170t-32t+300=0

We add all the numbers together, and all the variables

-16t^2-52t+300=0

a = -16; b = -52; c = +300;
Δ = b2-4ac
Δ = -522-4·(-16)·300
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-148}{2*-16}=\frac{-96}{-32}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+148}{2*-16}=\frac{200}{-32}
=-6+1/4
$