s+21/2s+20=50

Solution for s+21/2s+20=50 equation:

s+21/2s+20=50

We move all terms to the left:

s+21/2s+20-(50)=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-30=0

We multiply all the terms by the denominator


s*2s-30*2s+21=0

Wy multiply elements

2s^2-60s+21=0

a = 2; b = -60; c = +21;
Δ = b2-4ac
Δ = -602-4·2·21
Δ = 3432
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:

$\sqrt{\Delta}=\sqrt{3432}=\sqrt{4*858}=\sqrt{4}*\sqrt{858}=2\sqrt{858}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{858}}{2*2}=\frac{60-2\sqrt{858}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{858}}{2*2}=\frac{60+2\sqrt{858}}{4}
$