5v-10/v-6=2.5

Solution for 5v-10/v-6=2.5 equation:

5v-10/v-6=2.5

We move all terms to the left:

5v-10/v-6-(2.5)=0


Domain of the equation: v!=0

v∈R


We add all the numbers together, and all the variables

5v-10/v-8.5=0

We multiply all the terms by the denominator


5v*v-(8.5)*v-10=0

We multiply parentheses

5v*v-8.5v-10=0

Wy multiply elements

5v^2-8.5v-10=0

a = 5; b = -8.5; c = -10;
Δ = b2-4ac
Δ = -8.52-4·5·(-10)
Δ = 272.25
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{-(-8.5)-\sqrt{272.25}}{2*5}=\frac{8.5-\sqrt{272.25}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.5)+\sqrt{272.25}}{2*5}=\frac{8.5+\sqrt{272.25}}{10}
$