9=v+4/v+14

Solution for 9=v+4/v+14 equation:

9=v+4/v+14

We move all terms to the left:

9-(v+4/v+14)=0


Domain of the equation: v+14)!=0

v∈R


We get rid of parentheses

-v-4/v-14+9=0

We multiply all the terms by the denominator


-v*v-14*v+9*v-4=0

We add all the numbers together, and all the variables

-5v-v*v-4=0

Wy multiply elements

-1v^2-5v-4=0

a = -1; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·(-1)·(-4)
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{-(-5)-3}{2*-1}=\frac{2}{-2}
=-1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-1}=\frac{8}{-2}
=-4
$