s+31/2s+20s=56

Solution for s+31/2s+20s=56 equation:

s+31/2s+20s=56

We move all terms to the left:

s+31/2s+20s-(56)=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-56=0

We multiply all the terms by the denominator


21s*2s-56*2s+31=0

Wy multiply elements

42s^2-112s+31=0

a = 42; b = -112; c = +31;
Δ = b2-4ac
Δ = -1122-4·42·31
Δ = 7336
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:

$\sqrt{\Delta}=\sqrt{7336}=\sqrt{4*1834}=\sqrt{4}*\sqrt{1834}=2\sqrt{1834}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-2\sqrt{1834}}{2*42}=\frac{112-2\sqrt{1834}}{84}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+2\sqrt{1834}}{2*42}=\frac{112+2\sqrt{1834}}{84}
$