s+5=6/s

Solution for s+5=6/s equation:

s+5=6/s

We move all terms to the left:

s+5-(6/s)=0


Domain of the equation: s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

s-(+6/s)+5=0

We get rid of parentheses

s-6/s+5=0

We multiply all the terms by the denominator


s*s+5*s-6=0

We add all the numbers together, and all the variables

5s+s*s-6=0

Wy multiply elements

s^2+5s-6=0

a = 1; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*1}=\frac{-12}{2}
=-6
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*1}=\frac{2}{2}
=1
$