6s-4=892+1/4s

Solution for 6s-4=892+1/4s equation:

6s-4=892+1/4s

We move all terms to the left:

6s-4-(892+1/4s)=0


Domain of the equation: 4s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

6s-(1/4s+892)-4=0

We get rid of parentheses

6s-1/4s-892-4=0

We multiply all the terms by the denominator


6s*4s-892*4s-4*4s-1=0

Wy multiply elements

24s^2-3568s-16s-1=0

We add all the numbers together, and all the variables

24s^2-3584s-1=0

a = 24; b = -3584; c = -1;
Δ = b2-4ac
Δ = -35842-4·24·(-1)
Δ = 12845152
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:

$\sqrt{\Delta}=\sqrt{12845152}=\sqrt{16*802822}=\sqrt{16}*\sqrt{802822}=4\sqrt{802822}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3584)-4\sqrt{802822}}{2*24}=\frac{3584-4\sqrt{802822}}{48}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3584)+4\sqrt{802822}}{2*24}=\frac{3584+4\sqrt{802822}}{48}
$