t(2t+3)/t+6,t=-2

Solution for t(2t+3)/t+6,t=-2 equation:

t(2t+3)/t+6.t=-2

We move all terms to the left:

t(2t+3)/t+6.t-(-2)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

6.t+t(2t+3)/t+2=0

We multiply all the terms by the denominator


(6.t)*t+t(2t+3)+2*t=0

We add all the numbers together, and all the variables

(+6.t)*t+t(2t+3)+2*t=0

We add all the numbers together, and all the variables

2t+(+6.t)*t+t(2t+3)=0

We multiply parentheses

6t^2+2t^2+2t+3t=0

We add all the numbers together, and all the variables

8t^2+5t=0

a = 8; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·8·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*8}=\frac{-10}{16}
=-5/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*8}=\frac{0}{16}
=0
$