10/2v=-5v-50

Solution for 10/2v=-5v-50 equation:

10/2v=-5v-50

We move all terms to the left:

10/2v-(-5v-50)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We get rid of parentheses

10/2v+5v+50=0

We multiply all the terms by the denominator


5v*2v+50*2v+10=0

Wy multiply elements

10v^2+100v+10=0

a = 10; b = 100; c = +10;
Δ = b2-4ac
Δ = 1002-4·10·10
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-40\sqrt{6}}{2*10}=\frac{-100-40\sqrt{6}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+40\sqrt{6}}{2*10}=\frac{-100+40\sqrt{6}}{20}
$