s+3/12s+20=47

Solution for s+3/12s+20=47 equation:

s+3/12s+20=47

We move all terms to the left:

s+3/12s+20-(47)=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+3/12s-27=0

We multiply all the terms by the denominator


s*12s-27*12s+3=0

Wy multiply elements

12s^2-324s+3=0

a = 12; b = -324; c = +3;
Δ = b2-4ac
Δ = -3242-4·12·3
Δ = 104832
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:

$\sqrt{\Delta}=\sqrt{104832}=\sqrt{576*182}=\sqrt{576}*\sqrt{182}=24\sqrt{182}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-24\sqrt{182}}{2*12}=\frac{324-24\sqrt{182}}{24}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+24\sqrt{182}}{2*12}=\frac{324+24\sqrt{182}}{24}
$