x-1/x=2.25

Solution for x-1/x=2.25 equation:

x-1/x=2.25

We move all terms to the left:

x-1/x-(2.25)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-1/x-2.25=0

We multiply all the terms by the denominator


x*x-(2.25)*x-1=0

We multiply parentheses

x*x-2.25x-1=0

Wy multiply elements

x^2-2.25x-1=0

a = 1; b = -2.25; c = -1;
Δ = b2-4ac
Δ = -2.252-4·1·(-1)
Δ = 9.0625
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{-(-2.25)-\sqrt{9.0625}}{2*1}=\frac{2.25-\sqrt{9.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.25)+\sqrt{9.0625}}{2*1}=\frac{2.25+\sqrt{9.0625}}{2}
$