3/2t-16=4/3t-6

Solution for 3/2t-16=4/3t-6 equation:

3/2t-16=4/3t-6

We move all terms to the left:

3/2t-16-(4/3t-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

3/2t-4/3t+6-16=0

We calculate fractions


9t/6t^2+(-8t)/6t^2+6-16=0

We add all the numbers together, and all the variables

9t/6t^2+(-8t)/6t^2-10=0

We multiply all the terms by the denominator


9t+(-8t)-10*6t^2=0

Wy multiply elements

-60t^2+9t+(-8t)=0

We get rid of parentheses

-60t^2+9t-8t=0

We add all the numbers together, and all the variables

-60t^2+t=0

a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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