s+3+1/2s+20=6

Solution for s+3+1/2s+20=6 equation:

s+3+1/2s+20=6

We move all terms to the left:

s+3+1/2s+20-(6)=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+17=0

We multiply all the terms by the denominator


s*2s+17*2s+1=0

Wy multiply elements

2s^2+34s+1=0

a = 2; b = 34; c = +1;
Δ = b2-4ac
Δ = 342-4·2·1
Δ = 1148
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:

$\sqrt{\Delta}=\sqrt{1148}=\sqrt{4*287}=\sqrt{4}*\sqrt{287}=2\sqrt{287}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{287}}{2*2}=\frac{-34-2\sqrt{287}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{287}}{2*2}=\frac{-34+2\sqrt{287}}{4}
$