x^2*255=289

Solution for x^2*255=289 equation:

x^2*255=289

We move all terms to the left:

x^2*255-(289)=0

Wy multiply elements

255x^2-289=0

a = 255; b = 0; c = -289;
Δ = b2-4ac
Δ = 02-4·255·(-289)
Δ = 294780
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:

$\sqrt{\Delta}=\sqrt{294780}=\sqrt{1156*255}=\sqrt{1156}*\sqrt{255}=34\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{255}}{2*255}=\frac{0-34\sqrt{255}}{510}
=-\frac{34\sqrt{255}}{510}
=-\frac{\sqrt{255}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{255}}{2*255}=\frac{0+34\sqrt{255}}{510}
=\frac{34\sqrt{255}}{510}
=\frac{\sqrt{255}}{15}
$