x-3/x=0.81

Solution for x-3/x=0.81 equation:

x-3/x=0.81

We move all terms to the left:

x-3/x-(0.81)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-3/x-0.81=0

We multiply all the terms by the denominator


x*x-(0.81)*x-3=0

We multiply parentheses

x*x-0.81x-3=0

Wy multiply elements

x^2-0.81x-3=0

a = 1; b = -0.81; c = -3;
Δ = b2-4ac
Δ = -0.812-4·1·(-3)
Δ = 12.6561
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{-(-0.81)-\sqrt{12.6561}}{2*1}=\frac{0.81-\sqrt{12.6561}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.81)+\sqrt{12.6561}}{2*1}=\frac{0.81+\sqrt{12.6561}}{2}
$