v=1/33.145^210

Solution for v=1/33.145^210 equation:

v=1/33.145^210

We move all terms to the left:

v-(1/33.145^210)=0

We get rid of parentheses

v-1/33.145^210=0

We multiply all the terms by the denominator


v*33.145^210-1=0

Wy multiply elements

33v^2-1=0

a = 33; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·33·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{33}}{2*33}=\frac{0-2\sqrt{33}}{66}
=-\frac{2\sqrt{33}}{66}
=-\frac{\sqrt{33}}{33}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{33}}{2*33}=\frac{0+2\sqrt{33}}{66}
=\frac{2\sqrt{33}}{66}
=\frac{\sqrt{33}}{33}
$