x(x/2)=34000

Solution for x(x/2)=34000 equation:

x(x/2)=34000

We move all terms to the left:

x(x/2)-(34000)=0

We add all the numbers together, and all the variables

x(+x/2)-34000=0

We multiply parentheses

x^2-34000=0

a = 1; b = 0; c = -34000;
Δ = b2-4ac
Δ = 02-4·1·(-34000)
Δ = 136000
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:

$\sqrt{\Delta}=\sqrt{136000}=\sqrt{1600*85}=\sqrt{1600}*\sqrt{85}=40\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{85}}{2*1}=\frac{0-40\sqrt{85}}{2}
=-\frac{40\sqrt{85}}{2}
=-20\sqrt{85}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{85}}{2*1}=\frac{0+40\sqrt{85}}{2}
=\frac{40\sqrt{85}}{2}
=20\sqrt{85}
$