s+5/2s+20=62

Solution for s+5/2s+20=62 equation:

s+5/2s+20=62

We move all terms to the left:

s+5/2s+20-(62)=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+5/2s-42=0

We multiply all the terms by the denominator


s*2s-42*2s+5=0

Wy multiply elements

2s^2-84s+5=0

a = 2; b = -84; c = +5;
Δ = b2-4ac
Δ = -842-4·2·5
Δ = 7016
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:

$\sqrt{\Delta}=\sqrt{7016}=\sqrt{4*1754}=\sqrt{4}*\sqrt{1754}=2\sqrt{1754}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1754}}{2*2}=\frac{84-2\sqrt{1754}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1754}}{2*2}=\frac{84+2\sqrt{1754}}{4}
$