0.5x^2=40

Solution for 0.5x^2=40 equation:

0.5x^2=40

We move all terms to the left:

0.5x^2-(40)=0

a = 0.5; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·0.5·(-40)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*0.5}=\frac{0-4\sqrt{5}}{1}
=-\frac{4\sqrt{5}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*0.5}=\frac{0+4\sqrt{5}}{1}
=\frac{4\sqrt{5}}{1}
$