5v^2-3=417

Solution for 5v^2-3=417 equation:

5v^2-3=417

We move all terms to the left:

5v^2-3-(417)=0

We add all the numbers together, and all the variables

5v^2-420=0

a = 5; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·5·(-420)
Δ = 8400
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:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{21}}{2*5}=\frac{0-20\sqrt{21}}{10}
=-\frac{20\sqrt{21}}{10}
=-2\sqrt{21}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{21}}{2*5}=\frac{0+20\sqrt{21}}{10}
=\frac{20\sqrt{21}}{10}
=2\sqrt{21}
$