8v^2-3=669

Solution for 8v^2-3=669 equation:

8v^2-3=669

We move all terms to the left:

8v^2-3-(669)=0

We add all the numbers together, and all the variables

8v^2-672=0

a = 8; b = 0; c = -672;
Δ = b2-4ac
Δ = 02-4·8·(-672)
Δ = 21504
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:

$\sqrt{\Delta}=\sqrt{21504}=\sqrt{1024*21}=\sqrt{1024}*\sqrt{21}=32\sqrt{21}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{21}}{2*8}=\frac{0-32\sqrt{21}}{16}
=-\frac{32\sqrt{21}}{16}
=-2\sqrt{21}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{21}}{2*8}=\frac{0+32\sqrt{21}}{16}
=\frac{32\sqrt{21}}{16}
=2\sqrt{21}
$