s+31/2s+20=6

Solution for s+31/2s+20=6 equation:

s+31/2s+20=6

We move all terms to the left:

s+31/2s+20-(6)=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+14=0

We multiply all the terms by the denominator


s*2s+14*2s+31=0

Wy multiply elements

2s^2+28s+31=0

a = 2; b = 28; c = +31;
Δ = b2-4ac
Δ = 282-4·2·31
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{134}}{2*2}=\frac{-28-2\sqrt{134}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{134}}{2*2}=\frac{-28+2\sqrt{134}}{4}
$