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1/2s=4s
We move all terms to the left:
1/2s-(4s)=0
Domain of the equation: 2s!=0We add all the numbers together, and all the variables
s!=0/2
s!=0
s∈R
-4s+1/2s=0
We multiply all the terms by the denominator
-4s*2s+1=0
Wy multiply elements
-8s^2+1=0
a = -8; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-8)·1
Δ = 32
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{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*-8}=\frac{0-4\sqrt{2}}{-16} =-\frac{4\sqrt{2}}{-16} =-\frac{\sqrt{2}}{-4}s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*-8}=\frac{0+4\sqrt{2}}{-16} =\frac{4\sqrt{2}}{-16} =\frac{\sqrt{2}}{-4}
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