s+(2+1/2)s+10=31

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Solution for s+(2+1/2)s+10=31 equation:



s+(2+1/2)s+10=31
We move all terms to the left:
s+(2+1/2)s+10-(31)=0
Domain of the equation: 2)s!=0
s!=0/1
s!=0
s∈R
We add all the numbers together, and all the variables
s+(1/2+2)s+10-31=0
We add all the numbers together, and all the variables
s+(1/2+2)s-21=0
We multiply parentheses
s^2+s+2s-21=0
We add all the numbers together, and all the variables
s^2+3s-21=0
a = 1; b = 3; c = -21;
Δ = b2-4ac
Δ = 32-4·1·(-21)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{93}}{2*1}=\frac{-3-\sqrt{93}}{2} $
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{93}}{2*1}=\frac{-3+\sqrt{93}}{2} $

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