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

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

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

We move all terms to the left:

s+3+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

s+1/2s-51=0

We multiply all the terms by the denominator


s*2s-51*2s+1=0

Wy multiply elements

2s^2-102s+1=0

a = 2; b = -102; c = +1;
Δ = b2-4ac
Δ = -1022-4·2·1
Δ = 10396
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:

$\sqrt{\Delta}=\sqrt{10396}=\sqrt{4*2599}=\sqrt{4}*\sqrt{2599}=2\sqrt{2599}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{2599}}{2*2}=\frac{102-2\sqrt{2599}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{2599}}{2*2}=\frac{102+2\sqrt{2599}}{4}
$