s+3s+1/2s+20=74

Solution for s+3s+1/2s+20=74 equation:

s+3s+1/2s+20=74

We move all terms to the left:

s+3s+1/2s+20-(74)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

4s+1/2s-54=0

We multiply all the terms by the denominator


4s*2s-54*2s+1=0

Wy multiply elements

8s^2-108s+1=0

a = 8; b = -108; c = +1;
Δ = b2-4ac
Δ = -1082-4·8·1
Δ = 11632
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:

$\sqrt{\Delta}=\sqrt{11632}=\sqrt{16*727}=\sqrt{16}*\sqrt{727}=4\sqrt{727}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{727}}{2*8}=\frac{108-4\sqrt{727}}{16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{727}}{2*8}=\frac{108+4\sqrt{727}}{16}
$