(x)*(x/2)=800

Solution for (x)*(x/2)=800 equation:

(x)(x/2)=800

We move all terms to the left:

(x)(x/2)-(800)=0

We add all the numbers together, and all the variables

x(+x/2)-800=0

We multiply parentheses

x^2-800=0

a = 1; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·1·(-800)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*1}=\frac{0-40\sqrt{2}}{2}
=-\frac{40\sqrt{2}}{2}
=-20\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*1}=\frac{0+40\sqrt{2}}{2}
=\frac{40\sqrt{2}}{2}
=20\sqrt{2}
$