1+x=4.5(1+1/x)

Solution for 1+x=4.5(1+1/x) equation:

1+x=4.5(1+1/x)

We move all terms to the left:

1+x-(4.5(1+1/x))=0


Domain of the equation: x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(4.5(1/x+1))+1=0

We multiply all the terms by the denominator


x*x+1*x+1))-(4.5(1+1))=0

We add all the numbers together, and all the variables

x*x+1*x+1))-(4.52)=0

We add all the numbers together, and all the variables

x+x*x=0

Wy multiply elements

x^2+x=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1}=\frac{0}{2}
=0
$