s+31/2s+20s=74

Solution for s+31/2s+20s=74 equation:

s+31/2s+20s=74

We move all terms to the left:

s+31/2s+20s-(74)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

21s+31/2s-74=0

We multiply all the terms by the denominator


21s*2s-74*2s+31=0

Wy multiply elements

42s^2-148s+31=0

a = 42; b = -148; c = +31;
Δ = b2-4ac
Δ = -1482-4·42·31
Δ = 16696
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:

$\sqrt{\Delta}=\sqrt{16696}=\sqrt{4*4174}=\sqrt{4}*\sqrt{4174}=2\sqrt{4174}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-2\sqrt{4174}}{2*42}=\frac{148-2\sqrt{4174}}{84}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+2\sqrt{4174}}{2*42}=\frac{148+2\sqrt{4174}}{84}
$