x-1.5=1/x

Solution for x-1.5=1/x equation:

x-1.5=1/x

We move all terms to the left:

x-1.5-(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-(+1/x)-1.5=0

We get rid of parentheses

x-1/x-1.5=0

We multiply all the terms by the denominator


x*x-(1.5)*x-1=0

We multiply parentheses

x*x-1.5x-1=0

Wy multiply elements

x^2-1.5x-1=0

a = 1; b = -1.5; c = -1;
Δ = b2-4ac
Δ = -1.52-4·1·(-1)
Δ = 6.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{6.25}}{2*1}=\frac{1.5-\sqrt{6.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{6.25}}{2*1}=\frac{1.5+\sqrt{6.25}}{2}
$