s+21/2s+10s=52

Solution for s+21/2s+10s=52 equation:

s+21/2s+10s=52

We move all terms to the left:

s+21/2s+10s-(52)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

11s+21/2s-52=0

We multiply all the terms by the denominator


11s*2s-52*2s+21=0

Wy multiply elements

22s^2-104s+21=0

a = 22; b = -104; c = +21;
Δ = b2-4ac
Δ = -1042-4·22·21
Δ = 8968
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:

$\sqrt{\Delta}=\sqrt{8968}=\sqrt{4*2242}=\sqrt{4}*\sqrt{2242}=2\sqrt{2242}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-2\sqrt{2242}}{2*22}=\frac{104-2\sqrt{2242}}{44}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+2\sqrt{2242}}{2*22}=\frac{104+2\sqrt{2242}}{44}
$