x^2+16-225=0

Solution for x^2+16-225=0 equation:

x^2+16-225=0

We add all the numbers together, and all the variables

x^2-209=0

a = 1; b = 0; c = -209;
Δ = b2-4ac
Δ = 02-4·1·(-209)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{209}}{2*1}=\frac{0-2\sqrt{209}}{2}
=-\frac{2\sqrt{209}}{2}
=-\sqrt{209}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{209}}{2*1}=\frac{0+2\sqrt{209}}{2}
=\frac{2\sqrt{209}}{2}
=\sqrt{209}
$