1s+31/2s+20=74

Solution for 1s+31/2s+20=74 equation:

1s+31/2s+20=74

We move all terms to the left:

1s+31/2s+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+31/2s-54=0

We multiply all the terms by the denominator


s*2s-54*2s+31=0

Wy multiply elements

2s^2-108s+31=0

a = 2; b = -108; c = +31;
Δ = b2-4ac
Δ = -1082-4·2·31
Δ = 11416
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:

$\sqrt{\Delta}=\sqrt{11416}=\sqrt{4*2854}=\sqrt{4}*\sqrt{2854}=2\sqrt{2854}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2854}}{2*2}=\frac{108-2\sqrt{2854}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2854}}{2*2}=\frac{108+2\sqrt{2854}}{4}
$