11/2t-16=11/3t-6

Solution for 11/2t-16=11/3t-6 equation:

11/2t-16=11/3t-6

We move all terms to the left:

11/2t-16-(11/3t-6)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 3t-6)!=0

t∈R


We get rid of parentheses

11/2t-11/3t+6-16=0

We calculate fractions


33t/6t^2+(-22t)/6t^2+6-16=0

We add all the numbers together, and all the variables

33t/6t^2+(-22t)/6t^2-10=0

We multiply all the terms by the denominator


33t+(-22t)-10*6t^2=0

Wy multiply elements

-60t^2+33t+(-22t)=0

We get rid of parentheses

-60t^2+33t-22t=0

We add all the numbers together, and all the variables

-60t^2+11t=0

a = -60; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-60)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-60}=\frac{-22}{-120}
=11/60
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-60}=\frac{0}{-120}
=0
$