4/v-2=-6/5v-10+1

Solution for 4/v-2=-6/5v-10+1 equation:

4/v-2=-6/5v-10+1

We move all terms to the left:

4/v-2-(-6/5v-10+1)=0


Domain of the equation: v!=0

v∈R



Domain of the equation: 5v-10+1)!=0

We move all terms containing v to the left, all other terms to the right

5v+1)!=10

v∈R


We add all the numbers together, and all the variables

4/v-(-6/5v-9)-2=0

We get rid of parentheses

4/v+6/5v+9-2=0

We calculate fractions


20v/5v^2+6v/5v^2+9-2=0

We add all the numbers together, and all the variables

20v/5v^2+6v/5v^2+7=0

We multiply all the terms by the denominator


20v+6v+7*5v^2=0

We add all the numbers together, and all the variables

26v+7*5v^2=0

Wy multiply elements

35v^2+26v=0

a = 35; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·35·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*35}=\frac{-52}{70}
=-26/35
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*35}=\frac{0}{70}
=0
$