-2/3t-6-1/36=-3/4t-8

Solution for -2/3t-6-1/36=-3/4t-8 equation:

-2/3t-6-1/36=-3/4t-8

We move all terms to the left:

-2/3t-6-1/36-(-3/4t-8)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 4t-8)!=0

t∈R


We get rid of parentheses

-2/3t+3/4t+8-6-1/36=0

We calculate fractions


(-48t^2)/1296t^2+(-864t)/1296t^2+972t/1296t^2+8-6=0

We add all the numbers together, and all the variables

(-48t^2)/1296t^2+(-864t)/1296t^2+972t/1296t^2+2=0

We multiply all the terms by the denominator


(-48t^2)+(-864t)+972t+2*1296t^2=0

We add all the numbers together, and all the variables

(-48t^2)+972t+(-864t)+2*1296t^2=0

Wy multiply elements

(-48t^2)+2592t^2+972t+(-864t)=0

We get rid of parentheses

-48t^2+2592t^2+972t-864t=0

We add all the numbers together, and all the variables

2544t^2+108t=0

a = 2544; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·2544·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*2544}=\frac{-216}{5088}
=-9/212
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*2544}=\frac{0}{5088}
=0
$