v+21/v=-10

Solution for v+21/v=-10 equation:

v+21/v=-10

We move all terms to the left:

v+21/v-(-10)=0


Domain of the equation: v!=0

v∈R


We add all the numbers together, and all the variables

v+21/v+10=0

We multiply all the terms by the denominator


v*v+10*v+21=0

We add all the numbers together, and all the variables

10v+v*v+21=0

Wy multiply elements

v^2+10v+21=0

a = 1; b = 10; c = +21;
Δ = b2-4ac
Δ = 102-4·1·21
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*1}=\frac{-14}{2}
=-7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*1}=\frac{-6}{2}
=-3
$