6/2=v-10/v-1

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

6/2=v-10/v-1

We move all terms to the left:

6/2-(v-10/v-1)=0


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

v∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-v+10/v+1+3=0

We multiply all the terms by the denominator


-v*v+1*v+3*v+10=0

We add all the numbers together, and all the variables

4v-v*v+10=0

Wy multiply elements

-1v^2+4v+10=0

a = -1; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-1)·10
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*-1}=\frac{-4-2\sqrt{14}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*-1}=\frac{-4+2\sqrt{14}}{-2}
$