x(3/2)=6000

Solution for x(3/2)=6000 equation:

x(3/2)=6000

We move all terms to the left:

x(3/2)-(6000)=0

We add all the numbers together, and all the variables

x(+3/2)-6000=0

We multiply parentheses

3x^2-6000=0

a = 3; b = 0; c = -6000;
Δ = b2-4ac
Δ = 02-4·3·(-6000)
Δ = 72000
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:

$\sqrt{\Delta}=\sqrt{72000}=\sqrt{14400*5}=\sqrt{14400}*\sqrt{5}=120\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{5}}{2*3}=\frac{0-120\sqrt{5}}{6}
=-\frac{120\sqrt{5}}{6}
=-20\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{5}}{2*3}=\frac{0+120\sqrt{5}}{6}
=\frac{120\sqrt{5}}{6}
=20\sqrt{5}
$