s+7/s=-8

Solution for s+7/s=-8 equation:

s+7/s=-8

We move all terms to the left:

s+7/s-(-8)=0


Domain of the equation: s!=0

s∈R


We add all the numbers together, and all the variables

s+7/s+8=0

We multiply all the terms by the denominator


s*s+8*s+7=0

We add all the numbers together, and all the variables

8s+s*s+7=0

Wy multiply elements

s^2+8s+7=0

a = 1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·1·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*1}=\frac{-14}{2}
=-7
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*1}=\frac{-2}{2}
=-1
$