.2s+3s+2=6/2s

Solution for .2s+3s+2=6/2s equation:

.2s+3s+2=6/2s

We move all terms to the left:

.2s+3s+2-(6/2s)=0


Domain of the equation: 2s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

.2s+3s-(+6/2s)+2=0

We add all the numbers together, and all the variables

3.2s-(+6/2s)+2=0

We get rid of parentheses

3.2s-6/2s+2=0

We multiply all the terms by the denominator


(3.2s)*2s+2*2s-6=0

We add all the numbers together, and all the variables

(+3.2s)*2s+2*2s-6=0

We multiply parentheses

6s^2+2*2s-6=0

Wy multiply elements

6s^2+4s-6=0

a = 6; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·6·(-6)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*6}=\frac{-4-4\sqrt{10}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*6}=\frac{-4+4\sqrt{10}}{12}
$