s+1/4s=-7.25

Solution for s+1/4s=-7.25 equation:

s+1/4s=-7.25

We move all terms to the left:

s+1/4s-(-7.25)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We add all the numbers together, and all the variables

s+1/4s+7.25=0

We multiply all the terms by the denominator


s*4s+(7.25)*4s+1=0

We multiply parentheses

s*4s+29s+1=0

Wy multiply elements

4s^2+29s+1=0

a = 4; b = 29; c = +1;
Δ = b2-4ac
Δ = 292-4·4·1
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-5\sqrt{33}}{2*4}=\frac{-29-5\sqrt{33}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+5\sqrt{33}}{2*4}=\frac{-29+5\sqrt{33}}{8}
$