1444+x^2=(18x)^2

Solution for 1444+x^2=(18x)^2 equation:

1444+x^2=(18x)^2

We move all terms to the left:

1444+x^2-((18x)^2)=0

determiningTheFunctionDomain
x^2-18x^2+1444=0

We add all the numbers together, and all the variables

-17x^2+1444=0

a = -17; b = 0; c = +1444;
Δ = b2-4ac
Δ = 02-4·(-17)·1444
Δ = 98192
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:

$\sqrt{\Delta}=\sqrt{98192}=\sqrt{5776*17}=\sqrt{5776}*\sqrt{17}=76\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-76\sqrt{17}}{2*-17}=\frac{0-76\sqrt{17}}{-34}
=-\frac{76\sqrt{17}}{-34}
=-\frac{38\sqrt{17}}{-17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+76\sqrt{17}}{2*-17}=\frac{0+76\sqrt{17}}{-34}
=\frac{76\sqrt{17}}{-34}
=\frac{38\sqrt{17}}{-17}
$