1/7s+3+1/7s-3+s=180

Solution for 1/7s+3+1/7s-3+s=180 equation:

1/7s+3+1/7s-3+s=180

We move all terms to the left:

1/7s+3+1/7s-3+s-(180)=0


Domain of the equation: 7s!=0

s!=0/7

s!=0

s∈R


We add all the numbers together, and all the variables

s+1/7s+1/7s-180=0

We multiply all the terms by the denominator


s*7s-180*7s+1+1=0

We add all the numbers together, and all the variables

s*7s-180*7s+2=0

Wy multiply elements

7s^2-1260s+2=0

a = 7; b = -1260; c = +2;
Δ = b2-4ac
Δ = -12602-4·7·2
Δ = 1587544
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:

$\sqrt{\Delta}=\sqrt{1587544}=\sqrt{4*396886}=\sqrt{4}*\sqrt{396886}=2\sqrt{396886}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-2\sqrt{396886}}{2*7}=\frac{1260-2\sqrt{396886}}{14}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+2\sqrt{396886}}{2*7}=\frac{1260+2\sqrt{396886}}{14}
$