X2+(16.667x)2=324

Solution for X2+(16.667x)2=324 equation:

X2+(16.667X)2=324

We move all terms to the left:

X2+(16.667X)2-(324)=0

We add all the numbers together, and all the variables

X2+(+16.667X)2-324=0

We add all the numbers together, and all the variables

X^2+(+16.667X)2-324=0

We multiply parentheses

X^2+32X-324=0

a = 1; b = 32; c = -324;
Δ = b2-4ac
Δ = 322-4·1·(-324)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{145}}{2*1}=\frac{-32-4\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{145}}{2*1}=\frac{-32+4\sqrt{145}}{2}
$