-6+1/2v=7v+2

Solution for -6+1/2v=7v+2 equation:

-6+1/2v=7v+2

We move all terms to the left:

-6+1/2v-(7v+2)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We get rid of parentheses

1/2v-7v-2-6=0

We multiply all the terms by the denominator


-7v*2v-2*2v-6*2v+1=0

Wy multiply elements

-14v^2-4v-12v+1=0

We add all the numbers together, and all the variables

-14v^2-16v+1=0

a = -14; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-14)·1
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{78}}{2*-14}=\frac{16-2\sqrt{78}}{-28}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{78}}{2*-14}=\frac{16+2\sqrt{78}}{-28}
$