1+x^2=30.25

Solution for 1+x^2=30.25 equation:

1+x^2=30.25

We move all terms to the left:

1+x^2-(30.25)=0

We add all the numbers together, and all the variables

x^2-29.25=0

a = 1; b = 0; c = -29.25;
Δ = b2-4ac
Δ = 02-4·1·(-29.25)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{13}}{2*1}=\frac{0-3\sqrt{13}}{2}
=-\frac{3\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{13}}{2*1}=\frac{0+3\sqrt{13}}{2}
=\frac{3\sqrt{13}}{2}
$