-4t*(3/t+1)=-1

Solution for -4t*(3/t+1)=-1 equation:

-4t(3/t+1)=-1

We move all terms to the left:

-4t(3/t+1)-(-1)=0


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

t∈R


We add all the numbers together, and all the variables

-4t(3/t+1)+1=0

We multiply parentheses

-12t^2-4t+1=0

a = -12; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-12)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-12}=\frac{-4}{-24}
=1/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-12}=\frac{12}{-24}
=-1/2
$