(1/3)(v+9)=8

Solution for (1/3)(v+9)=8 equation:

(1/3)(v+9)=8

We move all terms to the left:

(1/3)(v+9)-(8)=0


Domain of the equation: 3)(v+9)!=0

v∈R


We add all the numbers together, and all the variables

(+1/3)(v+9)-8=0

We multiply parentheses ..

(+v^2+1/3*9)-8=0

We multiply all the terms by the denominator


(+v^2+1-8*3*9)=0

We get rid of parentheses

v^2+1-8*3*9=0

We add all the numbers together, and all the variables

v^2-215=0

a = 1; b = 0; c = -215;
Δ = b2-4ac
Δ = 02-4·1·(-215)
Δ = 860
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:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{215}}{2*1}=\frac{0-2\sqrt{215}}{2}
=-\frac{2\sqrt{215}}{2}
=-\sqrt{215}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{215}}{2*1}=\frac{0+2\sqrt{215}}{2}
=\frac{2\sqrt{215}}{2}
=\sqrt{215}
$