v+3/v-5=0

Solution for v+3/v-5=0 equation:

v+3/v-5=0


Domain of the equation: v!=0

v∈R


We multiply all the terms by the denominator


v*v-5*v+3=0

We add all the numbers together, and all the variables

-5v+v*v+3=0

Wy multiply elements

v^2-5v+3=0

a = 1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·1·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{13}}{2*1}=\frac{5-\sqrt{13}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*1}=\frac{5+\sqrt{13}}{2}
$