4s^2+9-125=0

Solution for 4s^2+9-125=0 equation:

4s^2+9-125=0

We add all the numbers together, and all the variables

4s^2-116=0

a = 4; b = 0; c = -116;
Δ = b2-4ac
Δ = 02-4·4·(-116)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{29}}{2*4}=\frac{0-8\sqrt{29}}{8}
=-\frac{8\sqrt{29}}{8}
=-\sqrt{29}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{29}}{2*4}=\frac{0+8\sqrt{29}}{8}
=\frac{8\sqrt{29}}{8}
=\sqrt{29}
$