.5x^2=128

Solution for .5x^2=128 equation:

.5x^2=128

We move all terms to the left:

.5x^2-(128)=0

a = .5; b = 0; c = -128;
Δ = b2-4ac
Δ = 02-4·.5·(-128)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*.5}=\frac{-16}{1}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*.5}=\frac{16}{1}
=16
$