s+9/s=-10

Solution for s+9/s=-10 equation:

s+9/s=-10

We move all terms to the left:

s+9/s-(-10)=0


Domain of the equation: s!=0

s∈R


We add all the numbers together, and all the variables

s+9/s+10=0

We multiply all the terms by the denominator


s*s+10*s+9=0

We add all the numbers together, and all the variables

10s+s*s+9=0

Wy multiply elements

s^2+10s+9=0

a = 1; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·1·9
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*1}=\frac{-18}{2}
=-9
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*1}=\frac{-2}{2}
=-1
$