1/4s+24=-1/2s

Solution for 1/4s+24=-1/2s equation:

1/4s+24=-1/2s

We move all terms to the left:

1/4s+24-(-1/2s)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R



Domain of the equation: 2s)!=0

s!=0/1

s!=0

s∈R


We get rid of parentheses

1/4s+1/2s+24=0

We calculate fractions


2s/8s^2+4s/8s^2+24=0

We multiply all the terms by the denominator


2s+4s+24*8s^2=0

We add all the numbers together, and all the variables

6s+24*8s^2=0

Wy multiply elements

192s^2+6s=0

a = 192; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·192·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*192}=\frac{-12}{384}
=-1/32
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*192}=\frac{0}{384}
=0
$