1/2s=4s-21*

Solution for 1/2s=4s-21* equation:

1/2s=4s-21*

We move all terms to the left:

1/2s-(4s-21*)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

1/2s-(+4s)=0

We get rid of parentheses

1/2s-4s=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}
$