x(.5x)=1800

Solution for x(.5x)=1800 equation:

x(.5x)=1800

We move all terms to the left:

x(.5x)-(1800)=0

We add all the numbers together, and all the variables

x(+.5x)-1800=0

We multiply parentheses

x^2-1800=0

a = 1; b = 0; c = -1800;
Δ = b2-4ac
Δ = 02-4·1·(-1800)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*1}=\frac{0-60\sqrt{2}}{2}
=-\frac{60\sqrt{2}}{2}
=-30\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*1}=\frac{0+60\sqrt{2}}{2}
=\frac{60\sqrt{2}}{2}
=30\sqrt{2}
$