-3/5v-10+1=5/v-2

Solution for -3/5v-10+1=5/v-2 equation:

-3/5v-10+1=5/v-2

We move all terms to the left:

-3/5v-10+1-(5/v-2)=0


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: v-2)!=0

v∈R


We add all the numbers together, and all the variables

-3/5v-(5/v-2)-9=0

We get rid of parentheses

-3/5v-5/v+2-9=0

We calculate fractions


(-3v)/5v^2+(-25v)/5v^2+2-9=0

We add all the numbers together, and all the variables

(-3v)/5v^2+(-25v)/5v^2-7=0

We multiply all the terms by the denominator


(-3v)+(-25v)-7*5v^2=0

Wy multiply elements

-35v^2+(-3v)+(-25v)=0

We get rid of parentheses

-35v^2-3v-25v=0

We add all the numbers together, and all the variables

-35v^2-28v=0

a = -35; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-35)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-35}=\frac{0}{-70}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-35}=\frac{56}{-70}
=-4/5
$