2/3s-9=1/2s-7

Solution for 2/3s-9=1/2s-7 equation:

2/3s-9=1/2s-7

We move all terms to the left:

2/3s-9-(1/2s-7)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R



Domain of the equation: 2s-7)!=0

s∈R


We get rid of parentheses

2/3s-1/2s+7-9=0

We calculate fractions


4s/6s^2+(-3s)/6s^2+7-9=0

We add all the numbers together, and all the variables

4s/6s^2+(-3s)/6s^2-2=0

We multiply all the terms by the denominator


4s+(-3s)-2*6s^2=0

Wy multiply elements

-12s^2+4s+(-3s)=0

We get rid of parentheses

-12s^2+4s-3s=0

We add all the numbers together, and all the variables

-12s^2+s=0

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

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