2x-5/x=1.8

Solution for 2x-5/x=1.8 equation:

2x-5/x=1.8

We move all terms to the left:

2x-5/x-(1.8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-5/x-1.8=0

We multiply all the terms by the denominator


2x*x-(1.8)*x-5=0

We multiply parentheses

2x*x-1.8x-5=0

Wy multiply elements

2x^2-1.8x-5=0

a = 2; b = -1.8; c = -5;
Δ = b2-4ac
Δ = -1.82-4·2·(-5)
Δ = 43.24
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{-(-1.8)-\sqrt{43.24}}{2*2}=\frac{1.8-\sqrt{43.24}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.8)+\sqrt{43.24}}{2*2}=\frac{1.8+\sqrt{43.24}}{4}
$