s+31/2s+10s=37

Solution for s+31/2s+10s=37 equation:

s+31/2s+10s=37

We move all terms to the left:

s+31/2s+10s-(37)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

11s+31/2s-37=0

We multiply all the terms by the denominator


11s*2s-37*2s+31=0

Wy multiply elements

22s^2-74s+31=0

a = 22; b = -74; c = +31;
Δ = b2-4ac
Δ = -742-4·22·31
Δ = 2748
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:

$\sqrt{\Delta}=\sqrt{2748}=\sqrt{4*687}=\sqrt{4}*\sqrt{687}=2\sqrt{687}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{687}}{2*22}=\frac{74-2\sqrt{687}}{44}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{687}}{2*22}=\frac{74+2\sqrt{687}}{44}
$