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

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

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

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 3t-6+16)!=0

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

3t+16)!=6

t∈R


We add all the numbers together, and all the variables

3/2t-(4/3t+10)-16+16=0

We add all the numbers together, and all the variables

3/2t-(4/3t+10)=0

We get rid of parentheses

3/2t-4/3t-10=0

We calculate fractions


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
$