v^2-8=3-5v^2

Solution for v^2-8=3-5v^2 equation:

v^2-8=3-5v^2

We move all terms to the left:

v^2-8-(3-5v^2)=0

We get rid of parentheses

v^2+5v^2-3-8=0

We add all the numbers together, and all the variables

6v^2-11=0

a = 6; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·6·(-11)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*6}=\frac{0-2\sqrt{66}}{12}
=-\frac{2\sqrt{66}}{12}
=-\frac{\sqrt{66}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*6}=\frac{0+2\sqrt{66}}{12}
=\frac{2\sqrt{66}}{12}
=\frac{\sqrt{66}}{6}
$