s+2+1/2s+20=62

Solution for s+2+1/2s+20=62 equation:

s+2+1/2s+20=62

We move all terms to the left:

s+2+1/2s+20-(62)=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-40=0

We multiply all the terms by the denominator


s*2s-40*2s+1=0

Wy multiply elements

2s^2-80s+1=0

a = 2; b = -80; c = +1;
Δ = b2-4ac
Δ = -802-4·2·1
Δ = 6392
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:

$\sqrt{\Delta}=\sqrt{6392}=\sqrt{4*1598}=\sqrt{4}*\sqrt{1598}=2\sqrt{1598}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1598}}{2*2}=\frac{80-2\sqrt{1598}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1598}}{2*2}=\frac{80+2\sqrt{1598}}{4}
$