.5v^2=10

Solution for .5v^2=10 equation:

.5v^2=10

We move all terms to the left:

.5v^2-(10)=0

a = .5; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·.5·(-10)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*.5}=\frac{0-2\sqrt{5}}{1}
=-\frac{2\sqrt{5}}{1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*.5}=\frac{0+2\sqrt{5}}{1}
=\frac{2\sqrt{5}}{1}
$