1/4s+20=-0.5s-4

Solution for 1/4s+20=-0.5s-4 equation:

1/4s+20=-0.5s-4

We move all terms to the left:

1/4s+20-(-0.5s-4)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We get rid of parentheses

1/4s+0.5s+4+20=0

We multiply all the terms by the denominator


(0.5s)*4s+4*4s+20*4s+1=0

We add all the numbers together, and all the variables

(+0.5s)*4s+4*4s+20*4s+1=0

We multiply parentheses

0s^2+4*4s+20*4s+1=0

Wy multiply elements

0s^2+16s+80s+1=0

We add all the numbers together, and all the variables

s^2+96s+1=0

a = 1; b = 96; c = +1;
Δ = b2-4ac
Δ = 962-4·1·1
Δ = 9212
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:

$\sqrt{\Delta}=\sqrt{9212}=\sqrt{196*47}=\sqrt{196}*\sqrt{47}=14\sqrt{47}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-14\sqrt{47}}{2*1}=\frac{-96-14\sqrt{47}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+14\sqrt{47}}{2*1}=\frac{-96+14\sqrt{47}}{2}
$