1/4-3/2s+15/3=5/3s

Solution for 1/4-3/2s+15/3=5/3s equation:

1/4-3/2s+15/3=5/3s

We move all terms to the left:

1/4-3/2s+15/3-(5/3s)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 3s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

-3/2s-(+5/3s)+1/4+15/3=0

We add all the numbers together, and all the variables

-3/2s-(+5/3s)+5+1/4=0

We get rid of parentheses

-3/2s-5/3s+5+1/4=0

We calculate fractions


18s^2/96s^2+(-144s)/96s^2+(-160s)/96s^2+5=0

We multiply all the terms by the denominator


18s^2+(-144s)+(-160s)+5*96s^2=0

Wy multiply elements

18s^2+480s^2+(-144s)+(-160s)=0

We get rid of parentheses

18s^2+480s^2-144s-160s=0

We add all the numbers together, and all the variables

498s^2-304s=0

a = 498; b = -304; c = 0;
Δ = b2-4ac
Δ = -3042-4·498·0
Δ = 92416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{92416}=304$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-304)-304}{2*498}=\frac{0}{996}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-304)+304}{2*498}=\frac{608}{996}
=152/249
$