5/2s-s=3+3/2s

Solution for 5/2s-s=3+3/2s equation:

5/2s-s=3+3/2s

We move all terms to the left:

5/2s-s-(3+3/2s)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 2s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

5/2s-s-(3/2s+3)=0

We add all the numbers together, and all the variables

-1s+5/2s-(3/2s+3)=0

We get rid of parentheses

-1s+5/2s-3/2s-3=0

We multiply all the terms by the denominator


-1s*2s-3*2s+5-3=0

We add all the numbers together, and all the variables

-1s*2s-3*2s+2=0

Wy multiply elements

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

a = -2; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-2)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-2}=\frac{6-2\sqrt{13}}{-4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-2}=\frac{6+2\sqrt{13}}{-4}
$