7/2+5/s-2=7/8s

Solution for 7/2+5/s-2=7/8s equation:

7/2+5/s-2=7/8s

We move all terms to the left:

7/2+5/s-2-(7/8s)=0


Domain of the equation: s!=0

s∈R



Domain of the equation: 8s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

5/s-(+7/8s)-2+7/2=0

We get rid of parentheses

5/s-7/8s-2+7/2=0

We calculate fractions


448s^2/32s^2+160s/32s^2+(-28s)/32s^2-2=0

We multiply all the terms by the denominator


448s^2+160s+(-28s)-2*32s^2=0

Wy multiply elements

448s^2-64s^2+160s+(-28s)=0

We get rid of parentheses

448s^2-64s^2+160s-28s=0

We add all the numbers together, and all the variables

384s^2+132s=0

a = 384; b = 132; c = 0;
Δ = b2-4ac
Δ = 1322-4·384·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-132}{2*384}=\frac{-264}{768}
=-11/32
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+132}{2*384}=\frac{0}{768}
=0
$