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

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

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

We move all terms to the left:

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


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6t^2+9t+6t-1=0

We add all the numbers together, and all the variables

6t^2+15t-1=0

a = 6; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·6·(-1)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{249}}{2*6}=\frac{-15-\sqrt{249}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*6}=\frac{-15+\sqrt{249}}{12}
$