x(11/4)=38000

Solution for x(11/4)=38000 equation:

x(11/4)=38000

We move all terms to the left:

x(11/4)-(38000)=0

We add all the numbers together, and all the variables

x(+11/4)-38000=0

We multiply parentheses

11x^2-38000=0

a = 11; b = 0; c = -38000;
Δ = b2-4ac
Δ = 02-4·11·(-38000)
Δ = 1672000
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:

$\sqrt{\Delta}=\sqrt{1672000}=\sqrt{1600*1045}=\sqrt{1600}*\sqrt{1045}=40\sqrt{1045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{1045}}{2*11}=\frac{0-40\sqrt{1045}}{22}
=-\frac{40\sqrt{1045}}{22}
=-\frac{20\sqrt{1045}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{1045}}{2*11}=\frac{0+40\sqrt{1045}}{22}
=\frac{40\sqrt{1045}}{22}
=\frac{20\sqrt{1045}}{11}
$