7/v-6=-5/2v-12+4

Solution for 7/v-6=-5/2v-12+4 equation:

7/v-6=-5/2v-12+4

We move all terms to the left:

7/v-6-(-5/2v-12+4)=0


Domain of the equation: v!=0

v∈R



Domain of the equation: 2v-12+4)!=0

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

2v+4)!=12

v∈R


We add all the numbers together, and all the variables

7/v-(-5/2v-8)-6=0

We get rid of parentheses

7/v+5/2v+8-6=0

We calculate fractions


14v/2v^2+5v/2v^2+8-6=0

We add all the numbers together, and all the variables

14v/2v^2+5v/2v^2+2=0

We multiply all the terms by the denominator


14v+5v+2*2v^2=0

We add all the numbers together, and all the variables

19v+2*2v^2=0

Wy multiply elements

4v^2+19v=0

a = 4; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·4·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*4}=\frac{-38}{8}
=-4+3/4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*4}=\frac{0}{8}
=0
$