x-(1/x)=0.75

Solution for x-(1/x)=0.75 equation:

x-(1/x)=0.75

We move all terms to the left:

x-(1/x)-(0.75)=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)-(0.75)=0

We add all the numbers together, and all the variables

x-(+1/x)-0.75=0

We get rid of parentheses

x-1/x-0.75=0

We multiply all the terms by the denominator


x*x-(0.75)*x-1=0

We multiply parentheses

x*x-0.75x-1=0

Wy multiply elements

x^2-0.75x-1=0

a = 1; b = -0.75; c = -1;
Δ = b2-4ac
Δ = -0.752-4·1·(-1)
Δ = 4.5625
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{-(-0.75)-\sqrt{4.5625}}{2*1}=\frac{0.75-\sqrt{4.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.75)+\sqrt{4.5625}}{2*1}=\frac{0.75+\sqrt{4.5625}}{2}
$