75000/v=125.5+0.527*v^2

Solution for 75000/v=125.5+0.527*v^2 equation:

75000/v=125.5+0.527v^2

We move all terms to the left:

75000/v-(125.5+0.527v^2)=0


Domain of the equation: v!=0

v∈R


We get rid of parentheses

-0.527v^2+75000/v-125.5=0

We multiply all the terms by the denominator


-(0.527v^2)*v-(125.5)*v+75000=0

We multiply parentheses

-0v^2-125.5v+75000=0

We add all the numbers together, and all the variables

-1v^2-125.5v+75000=0

a = -1; b = -125.5; c = +75000;
Δ = b2-4ac
Δ = -125.52-4·(-1)·75000
Δ = 315750.25
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{-(-125.5)-\sqrt{315750.25}}{2*-1}=\frac{125.5-\sqrt{315750.25}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125.5)+\sqrt{315750.25}}{2*-1}=\frac{125.5+\sqrt{315750.25}}{-2}
$