v2=465

Solution for v2=465 equation:

v2=465

We move all terms to the left:

v2-(465)=0

We add all the numbers together, and all the variables

v^2-465=0

a = 1; b = 0; c = -465;
Δ = b2-4ac
Δ = 02-4·1·(-465)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{465}}{2*1}=\frac{0-2\sqrt{465}}{2}
=-\frac{2\sqrt{465}}{2}
=-\sqrt{465}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{465}}{2*1}=\frac{0+2\sqrt{465}}{2}
=\frac{2\sqrt{465}}{2}
=\sqrt{465}
$