v-1/9v+6=11

Solution for v-1/9v+6=11 equation:

v-1/9v+6=11

We move all terms to the left:

v-1/9v+6-(11)=0


Domain of the equation: 9v!=0

v!=0/9

v!=0

v∈R


We add all the numbers together, and all the variables

v-1/9v-5=0

We multiply all the terms by the denominator


v*9v-5*9v-1=0

Wy multiply elements

9v^2-45v-1=0

a = 9; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·9·(-1)
Δ = 2061
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:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{229}}{2*9}=\frac{45-3\sqrt{229}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{229}}{2*9}=\frac{45+3\sqrt{229}}{18}
$