v^2=-36+16v

Solution for v^2=-36+16v equation:

v^2=-36+16v

We move all terms to the left:

v^2-(-36+16v)=0

We add all the numbers together, and all the variables

v^2-(16v-36)=0

We get rid of parentheses

v^2-16v+36=0

a = 1; b = -16; c = +36;
Δ = b2-4ac
Δ = -162-4·1·36
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*1}=\frac{16-4\sqrt{7}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*1}=\frac{16+4\sqrt{7}}{2}
$