9=v+4/v+4

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

9=v+4/v+4

We move all terms to the left:

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


Domain of the equation: v+4)!=0

v∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-v*v-4*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{-8}{-2}
=+4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2}
=1
$