s+3-1/2s+20=47

Solution for s+3-1/2s+20=47 equation:

s+3-1/2s+20=47

We move all terms to the left:

s+3-1/2s+20-(47)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

s-1/2s-24=0

We multiply all the terms by the denominator


s*2s-24*2s-1=0

Wy multiply elements

2s^2-48s-1=0

a = 2; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·2·(-1)
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-34\sqrt{2}}{2*2}=\frac{48-34\sqrt{2}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+34\sqrt{2}}{2*2}=\frac{48+34\sqrt{2}}{4}
$