s+21/2s+20=1

Solution for s+21/2s+20=1 equation:

s+21/2s+20=1

We move all terms to the left:

s+21/2s+20-(1)=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+21/2s+19=0

We multiply all the terms by the denominator


s*2s+19*2s+21=0

Wy multiply elements

2s^2+38s+21=0

a = 2; b = 38; c = +21;
Δ = b2-4ac
Δ = 382-4·2·21
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{319}}{2*2}=\frac{-38-2\sqrt{319}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{319}}{2*2}=\frac{-38+2\sqrt{319}}{4}
$