v+16=9-10/v

Solution for v+16=9-10/v equation:

v+16=9-10/v

We move all terms to the left:

v+16-(9-10/v)=0


Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

v-(-10/v+9)+16=0

We get rid of parentheses

v+10/v-9+16=0

We multiply all the terms by the denominator


v*v-9*v+16*v+10=0

We add all the numbers together, and all the variables

7v+v*v+10=0

Wy multiply elements

v^2+7v+10=0

a = 1; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*1}=\frac{-10}{2}
=-5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*1}=\frac{-4}{2}
=-2
$