5=2g+1/g

Solution for 5=2g+1/g equation:

5=2g+1/g

We move all terms to the left:

5-(2g+1/g)=0


Domain of the equation: g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

-(+2g+1/g)+5=0

We get rid of parentheses

-2g-1/g+5=0

We multiply all the terms by the denominator


-2g*g+5*g-1=0

We add all the numbers together, and all the variables

5g-2g*g-1=0

Wy multiply elements

-2g^2+5g-1=0

a = -2; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-2)·(-1)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{17}}{2*-2}=\frac{-5-\sqrt{17}}{-4}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{17}}{2*-2}=\frac{-5+\sqrt{17}}{-4}
$