s+2/12s+20=48

Solution for s+2/12s+20=48 equation:

s+2/12s+20=48

We move all terms to the left:

s+2/12s+20-(48)=0


Domain of the equation: 12s!=0

s!=0/12

s!=0

s∈R


We add all the numbers together, and all the variables

s+2/12s-28=0

We multiply all the terms by the denominator


s*12s-28*12s+2=0

Wy multiply elements

12s^2-336s+2=0

a = 12; b = -336; c = +2;
Δ = b2-4ac
Δ = -3362-4·12·2
Δ = 112800
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:

$\sqrt{\Delta}=\sqrt{112800}=\sqrt{400*282}=\sqrt{400}*\sqrt{282}=20\sqrt{282}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-20\sqrt{282}}{2*12}=\frac{336-20\sqrt{282}}{24}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+20\sqrt{282}}{2*12}=\frac{336+20\sqrt{282}}{24}
$