0.5*x-1.5/x=1.04

Solution for 0.5*x-1.5/x=1.04 equation:

0.5x-1.5/x=1.04

We move all terms to the left:

0.5x-1.5/x-(1.04)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

0.5x-1.5/x-1.04=0

We multiply all the terms by the denominator


(0.5x)*x-(1.04)*x-1.5=0

We add all the numbers together, and all the variables

(+0.5x)*x-(1.04)*x-1.5=0

We multiply parentheses

0x^2-1.04x-1.5=0

We add all the numbers together, and all the variables

x^2-1.04x-1.5=0

a = 1; b = -1.04; c = -1.5;
Δ = b2-4ac
Δ = -1.042-4·1·(-1.5)
Δ = 7.0816
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{-(-1.04)-\sqrt{7.0816}}{2*1}=\frac{1.04-\sqrt{7.0816}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.04)+\sqrt{7.0816}}{2*1}=\frac{1.04+\sqrt{7.0816}}{2}
$