s+31/2s+20=64

Solution for s+31/2s+20=64 equation:

s+31/2s+20=64

We move all terms to the left:

s+31/2s+20-(64)=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+31/2s-44=0

We multiply all the terms by the denominator


s*2s-44*2s+31=0

Wy multiply elements

2s^2-88s+31=0

a = 2; b = -88; c = +31;
Δ = b2-4ac
Δ = -882-4·2·31
Δ = 7496
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:

$\sqrt{\Delta}=\sqrt{7496}=\sqrt{4*1874}=\sqrt{4}*\sqrt{1874}=2\sqrt{1874}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-2\sqrt{1874}}{2*2}=\frac{88-2\sqrt{1874}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+2\sqrt{1874}}{2*2}=\frac{88+2\sqrt{1874}}{4}
$