x^2-45=400

Solution for x^2-45=400 equation:

x^2-45=400

We move all terms to the left:

x^2-45-(400)=0

We add all the numbers together, and all the variables

x^2-445=0

a = 1; b = 0; c = -445;
Δ = b2-4ac
Δ = 02-4·1·(-445)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{445}}{2*1}=\frac{0-2\sqrt{445}}{2}
=-\frac{2\sqrt{445}}{2}
=-\sqrt{445}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{445}}{2*1}=\frac{0+2\sqrt{445}}{2}
=\frac{2\sqrt{445}}{2}
=\sqrt{445}
$