s+5/4s+20=41

Solution for s+5/4s+20=41 equation:

s+5/4s+20=41

We move all terms to the left:

s+5/4s+20-(41)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We add all the numbers together, and all the variables

s+5/4s-21=0

We multiply all the terms by the denominator


s*4s-21*4s+5=0

Wy multiply elements

4s^2-84s+5=0

a = 4; b = -84; c = +5;
Δ = b2-4ac
Δ = -842-4·4·5
Δ = 6976
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:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-8\sqrt{109}}{2*4}=\frac{84-8\sqrt{109}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+8\sqrt{109}}{2*4}=\frac{84+8\sqrt{109}}{8}
$