2s+s+1/2s+9=65

Solution for 2s+s+1/2s+9=65 equation:

2s+s+1/2s+9=65

We move all terms to the left:

2s+s+1/2s+9-(65)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

3s+1/2s-56=0

We multiply all the terms by the denominator


3s*2s-56*2s+1=0

Wy multiply elements

6s^2-112s+1=0

a = 6; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·6·1
Δ = 12520
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:

$\sqrt{\Delta}=\sqrt{12520}=\sqrt{4*3130}=\sqrt{4}*\sqrt{3130}=2\sqrt{3130}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-2\sqrt{3130}}{2*6}=\frac{112-2\sqrt{3130}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+2\sqrt{3130}}{2*6}=\frac{112+2\sqrt{3130}}{12}
$