s^2-25=256

Solution for s^2-25=256 equation:

s^2-25=256

We move all terms to the left:

s^2-25-(256)=0

We add all the numbers together, and all the variables

s^2-281=0

a = 1; b = 0; c = -281;
Δ = b2-4ac
Δ = 02-4·1·(-281)
Δ = 1124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{281}}{2*1}=\frac{0-2\sqrt{281}}{2}
=-\frac{2\sqrt{281}}{2}
=-\sqrt{281}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{281}}{2*1}=\frac{0+2\sqrt{281}}{2}
=\frac{2\sqrt{281}}{2}
=\sqrt{281}
$