2/s-9=8/10s+9

Solution for 2/s-9=8/10s+9 equation:

2/s-9=8/10s+9

We move all terms to the left:

2/s-9-(8/10s+9)=0


Domain of the equation: s!=0

s∈R



Domain of the equation: 10s+9)!=0

s∈R


We get rid of parentheses

2/s-8/10s-9-9=0

We calculate fractions


20s/10s^2+(-8s)/10s^2-9-9=0

We add all the numbers together, and all the variables

20s/10s^2+(-8s)/10s^2-18=0

We multiply all the terms by the denominator


20s+(-8s)-18*10s^2=0

Wy multiply elements

-180s^2+20s+(-8s)=0

We get rid of parentheses

-180s^2+20s-8s=0

We add all the numbers together, and all the variables

-180s^2+12s=0

a = -180; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-180)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-180}=\frac{-24}{-360}
=1/15
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-180}=\frac{0}{-360}
=0
$