6(6v/6)-5=1/6v

Solution for 6(6v/6)-5=1/6v equation:

6(6v/6)-5=1/6v

We move all terms to the left:

6(6v/6)-5-(1/6v)=0


Domain of the equation: 6v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

6(+6v/6)-(+1/6v)-5=0

We multiply parentheses

36v-(+1/6v)-5=0

We get rid of parentheses

36v-1/6v-5=0

We multiply all the terms by the denominator


36v*6v-5*6v-1=0

Wy multiply elements

216v^2-30v-1=0

a = 216; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·216·(-1)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-42}{2*216}=\frac{-12}{432}
=-1/36
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+42}{2*216}=\frac{72}{432}
=1/6
$