4s-21=1/2s

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

4s-21=1/2s

We move all terms to the left:

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


Domain of the equation: 2s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4s-1/2s-21=0

We multiply all the terms by the denominator


4s*2s-21*2s-1=0

Wy multiply elements

8s^2-42s-1=0

a = 8; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·8·(-1)
Δ = 1796
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:

$\sqrt{\Delta}=\sqrt{1796}=\sqrt{4*449}=\sqrt{4}*\sqrt{449}=2\sqrt{449}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{449}}{2*8}=\frac{42-2\sqrt{449}}{16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{449}}{2*8}=\frac{42+2\sqrt{449}}{16}
$