x*x+1=483

Solution for x*x+1=483 equation:

x*x+1=483

We move all terms to the left:

x*x+1-(483)=0

We add all the numbers together, and all the variables

x*x-482=0

Wy multiply elements

x^2-482=0

a = 1; b = 0; c = -482;
Δ = b2-4ac
Δ = 02-4·1·(-482)
Δ = 1928
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:

$\sqrt{\Delta}=\sqrt{1928}=\sqrt{4*482}=\sqrt{4}*\sqrt{482}=2\sqrt{482}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{482}}{2*1}=\frac{0-2\sqrt{482}}{2}
=-\frac{2\sqrt{482}}{2}
=-\sqrt{482}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{482}}{2*1}=\frac{0+2\sqrt{482}}{2}
=\frac{2\sqrt{482}}{2}
=\sqrt{482}
$