s^2-5s-25/4=0

Solution for s^2-5s-25/4=0 equation:

s^2-5s-25/4=0

We multiply all the terms by the denominator


s^2*4-5s*4-25=0

Wy multiply elements

4s^2-20s-25=0

a = 4; b = -20; c = -25;
Δ = b2-4ac
Δ = -202-4·4·(-25)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{2}}{2*4}=\frac{20-20\sqrt{2}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{2}}{2*4}=\frac{20+20\sqrt{2}}{8}
$