81/4s+20=-1/2s-4

Solution for 81/4s+20=-1/2s-4 equation:

81/4s+20=-1/2s-4

We move all terms to the left:

81/4s+20-(-1/2s-4)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R



Domain of the equation: 2s-4)!=0

s∈R


We get rid of parentheses

81/4s+1/2s+4+20=0

We calculate fractions


162s/8s^2+4s/8s^2+4+20=0

We add all the numbers together, and all the variables

162s/8s^2+4s/8s^2+24=0

We multiply all the terms by the denominator


162s+4s+24*8s^2=0

We add all the numbers together, and all the variables

166s+24*8s^2=0

Wy multiply elements

192s^2+166s=0

a = 192; b = 166; c = 0;
Δ = b2-4ac
Δ = 1662-4·192·0
Δ = 27556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27556}=166$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(166)-166}{2*192}=\frac{-332}{384}
=-83/96
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(166)+166}{2*192}=\frac{0}{384}
=0
$