(2/3)s-(5/6)s+0.5=-3/2

Solution for (2/3)s-(5/6)s+0.5=-3/2 equation:

(2/3)s-(5/6)s+0.5=-3/2

We move all terms to the left:

(2/3)s-(5/6)s+0.5-(-3/2)=0


Domain of the equation: 3)s!=0

s!=0/1

s!=0

s∈R



Domain of the equation: 6)s!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

(+2/3)s-(+5/6)s+0.5-(-3/2)=0

We multiply parentheses

2s^2-5s^2+0.5-(-3/2)=0

We get rid of parentheses

2s^2-5s^2+0.5+3/2=0

We multiply all the terms by the denominator


2s^2*2-5s^2*2+3+(0.5)*2=0

We add all the numbers together, and all the variables

2s^2*2-5s^2*2+4=0

Wy multiply elements

4s^2-10s^2+4=0

We add all the numbers together, and all the variables

-6s^2+4=0

a = -6; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-6)·4
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-6}=\frac{0-4\sqrt{6}}{-12}
=-\frac{4\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-3}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-6}=\frac{0+4\sqrt{6}}{-12}
=\frac{4\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-3}
$