-3t-31=2/3t+1

Solution for -3t-31=2/3t+1 equation:

-3t-31=2/3t+1

We move all terms to the left:

-3t-31-(2/3t+1)=0


Domain of the equation: 3t+1)!=0

t∈R


We get rid of parentheses

-3t-2/3t-1-31=0

We multiply all the terms by the denominator


-3t*3t-1*3t-31*3t-2=0

Wy multiply elements

-9t^2-3t-93t-2=0

We add all the numbers together, and all the variables

-9t^2-96t-2=0

a = -9; b = -96; c = -2;
Δ = b2-4ac
Δ = -962-4·(-9)·(-2)
Δ = 9144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9144}=\sqrt{36*254}=\sqrt{36}*\sqrt{254}=6\sqrt{254}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-6\sqrt{254}}{2*-9}=\frac{96-6\sqrt{254}}{-18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+6\sqrt{254}}{2*-9}=\frac{96+6\sqrt{254}}{-18}
$