v^2=54-12v

Solution for v^2=54-12v equation:

v^2=54-12v

We move all terms to the left:

v^2-(54-12v)=0

We add all the numbers together, and all the variables

v^2-(-12v+54)=0

We get rid of parentheses

v^2+12v-54=0

a = 1; b = 12; c = -54;
Δ = b2-4ac
Δ = 122-4·1·(-54)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{10}}{2*1}=\frac{-12-6\sqrt{10}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{10}}{2*1}=\frac{-12+6\sqrt{10}}{2}
$