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

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

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

We move all terms to the left:

1/4s+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

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

We calculate fractions


2s/8s^2+(-4s)/8s^2+4+20=0

We add all the numbers together, and all the variables

2s/8s^2+(-4s)/8s^2+24=0

We multiply all the terms by the denominator


2s+(-4s)+24*8s^2=0

Wy multiply elements

192s^2+2s+(-4s)=0

We get rid of parentheses

192s^2+2s-4s=0

We add all the numbers together, and all the variables

192s^2-2s=0

a = 192; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·192·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*192}=\frac{0}{384}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*192}=\frac{4}{384}
=1/96
$