2-2s=3/48s+13

Solution for 2-2s=3/48s+13 equation:

2-2s=3/48s+13

We move all terms to the left:

2-2s-(3/48s+13)=0


Domain of the equation: 48s+13)!=0

s∈R


We get rid of parentheses

-2s-3/48s-13+2=0

We multiply all the terms by the denominator


-2s*48s-13*48s+2*48s-3=0

Wy multiply elements

-96s^2-624s+96s-3=0

We add all the numbers together, and all the variables

-96s^2-528s-3=0

a = -96; b = -528; c = -3;
Δ = b2-4ac
Δ = -5282-4·(-96)·(-3)
Δ = 277632
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:

$\sqrt{\Delta}=\sqrt{277632}=\sqrt{576*482}=\sqrt{576}*\sqrt{482}=24\sqrt{482}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-528)-24\sqrt{482}}{2*-96}=\frac{528-24\sqrt{482}}{-192}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-528)+24\sqrt{482}}{2*-96}=\frac{528+24\sqrt{482}}{-192}
$