1/6s-1/2s+1=45/2

Solution for 1/6s-1/2s+1=45/2 equation:

1/6s-1/2s+1=45/2

We move all terms to the left:

1/6s-1/2s+1-(45/2)=0


Domain of the equation: 6s!=0

s!=0/6

s!=0

s∈R



Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

1/6s-1/2s+1-(+45/2)=0

We get rid of parentheses

1/6s-1/2s+1-45/2=0

We calculate fractions


8s/48s^2+(-6s)/48s^2+(-270s)/48s^2+1=0

We multiply all the terms by the denominator


8s+(-6s)+(-270s)+1*48s^2=0

Wy multiply elements

48s^2+8s+(-6s)+(-270s)=0

We get rid of parentheses

48s^2+8s-6s-270s=0

We add all the numbers together, and all the variables

48s^2-268s=0

a = 48; b = -268; c = 0;
Δ = b2-4ac
Δ = -2682-4·48·0
Δ = 71824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{71824}=268$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-268)-268}{2*48}=\frac{0}{96}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-268)+268}{2*48}=\frac{536}{96}
=5+7/12
$