110=1/28v^2

Solution for 110=1/28v^2 equation:

110=1/28v^2

We move all terms to the left:

110-(1/28v^2)=0


Domain of the equation: 28v^2)!=0

v!=0/1

v!=0

v∈R


We get rid of parentheses

-1/28v^2+110=0

We multiply all the terms by the denominator


110*28v^2-1=0

Wy multiply elements

3080v^2-1=0

a = 3080; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·3080·(-1)
Δ = 12320
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:

$\sqrt{\Delta}=\sqrt{12320}=\sqrt{16*770}=\sqrt{16}*\sqrt{770}=4\sqrt{770}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{770}}{2*3080}=\frac{0-4\sqrt{770}}{6160}
=-\frac{4\sqrt{770}}{6160}
=-\frac{\sqrt{770}}{1540}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{770}}{2*3080}=\frac{0+4\sqrt{770}}{6160}
=\frac{4\sqrt{770}}{6160}
=\frac{\sqrt{770}}{1540}
$