t+6/t=-5

Solution for t+6/t=-5 equation:

t+6/t=-5

We move all terms to the left:

t+6/t-(-5)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

t+6/t+5=0

We multiply all the terms by the denominator


t*t+5*t+6=0

We add all the numbers together, and all the variables

5t+t*t+6=0

Wy multiply elements

t^2+5t+6=0

a = 1; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*1}=\frac{-6}{2}
=-3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*1}=\frac{-4}{2}
=-2
$