3/2s=24-7/6s

Solution for 3/2s=24-7/6s equation:

3/2s=24-7/6s

We move all terms to the left:

3/2s-(24-7/6s)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 6s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

3/2s-(-7/6s+24)=0

We get rid of parentheses

3/2s+7/6s-24=0

We calculate fractions


18s/12s^2+14s/12s^2-24=0

We multiply all the terms by the denominator


18s+14s-24*12s^2=0

We add all the numbers together, and all the variables

32s-24*12s^2=0

Wy multiply elements

-288s^2+32s=0

a = -288; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-288)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-288}=\frac{-64}{-576}
=1/9
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-288}=\frac{0}{-576}
=0
$