0.5a^2+4=a^2

Solution for 0.5a^2+4=a^2 equation:

0.5a^2+4=a^2

We move all terms to the left:

0.5a^2+4-(a^2)=0

We add all the numbers together, and all the variables

-0.5a^2+4=0

a = -0.5; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-0.5)·4
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-0.5}=\frac{0-2\sqrt{2}}{-1}
=-\frac{2\sqrt{2}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-0.5}=\frac{0+2\sqrt{2}}{-1}
=\frac{2\sqrt{2}}{-1}
$