s+(3)1/2s+20=65

Solution for s+(3)1/2s+20=65 equation:

s+(3)1/2s+20=65

We move all terms to the left:

s+(3)1/2s+20-(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

s+31/2s-45=0

We multiply all the terms by the denominator


s*2s-45*2s+31=0

Wy multiply elements

2s^2-90s+31=0

a = 2; b = -90; c = +31;
Δ = b2-4ac
Δ = -902-4·2·31
Δ = 7852
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:

$\sqrt{\Delta}=\sqrt{7852}=\sqrt{4*1963}=\sqrt{4}*\sqrt{1963}=2\sqrt{1963}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1963}}{2*2}=\frac{90-2\sqrt{1963}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1963}}{2*2}=\frac{90+2\sqrt{1963}}{4}
$