x(x+4)(x-4)=231

Solution for x(x+4)(x-4)=231 equation:

x(x+4)(x-4)=231

We move all terms to the left:

x(x+4)(x-4)-(231)=0

We use the square of the difference formula

x^2-16-231=0

We add all the numbers together, and all the variables

x^2-247=0

a = 1; b = 0; c = -247;
Δ = b2-4ac
Δ = 02-4·1·(-247)
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{247}}{2*1}=\frac{0-2\sqrt{247}}{2}
=-\frac{2\sqrt{247}}{2}
=-\sqrt{247}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{247}}{2*1}=\frac{0+2\sqrt{247}}{2}
=\frac{2\sqrt{247}}{2}
=\sqrt{247}
$