1/2s+3+s=39

Solution for 1/2s+3+s=39 equation:

1/2s+3+s=39

We move all terms to the left:

1/2s+3+s-(39)=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+1/2s-36=0

We multiply all the terms by the denominator


s*2s-36*2s+1=0

Wy multiply elements

2s^2-72s+1=0

a = 2; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·2·1
Δ = 5176
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:

$\sqrt{\Delta}=\sqrt{5176}=\sqrt{4*1294}=\sqrt{4}*\sqrt{1294}=2\sqrt{1294}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1294}}{2*2}=\frac{72-2\sqrt{1294}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1294}}{2*2}=\frac{72+2\sqrt{1294}}{4}
$