2/6v-1/7v+14=20

Solution for 2/6v-1/7v+14=20 equation:

2/6v-1/7v+14=20

We move all terms to the left:

2/6v-1/7v+14-(20)=0


Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R



Domain of the equation: 7v!=0

v!=0/7

v!=0

v∈R


We add all the numbers together, and all the variables

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

We calculate fractions


14v/42v^2+(-6v)/42v^2-6=0

We multiply all the terms by the denominator


14v+(-6v)-6*42v^2=0

Wy multiply elements

-252v^2+14v+(-6v)=0

We get rid of parentheses

-252v^2+14v-6v=0

We add all the numbers together, and all the variables

-252v^2+8v=0

a = -252; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-252)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-252}=\frac{-16}{-504}
=2/63
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-252}=\frac{0}{-504}
=0
$