x*x+1=306

Solution for x*x+1=306 equation:

x*x+1=306

We move all terms to the left:

x*x+1-(306)=0

We add all the numbers together, and all the variables

x*x-305=0

Wy multiply elements

x^2-305=0

a = 1; b = 0; c = -305;
Δ = b2-4ac
Δ = 02-4·1·(-305)
Δ = 1220
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:

$\sqrt{\Delta}=\sqrt{1220}=\sqrt{4*305}=\sqrt{4}*\sqrt{305}=2\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{305}}{2*1}=\frac{0-2\sqrt{305}}{2}
=-\frac{2\sqrt{305}}{2}
=-\sqrt{305}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{305}}{2*1}=\frac{0+2\sqrt{305}}{2}
=\frac{2\sqrt{305}}{2}
=\sqrt{305}
$