1.5x-4=2/x+1

Solution for 1.5x-4=2/x+1 equation:

1.5x-4=2/x+1

We move all terms to the left:

1.5x-4-(2/x+1)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

1.5x-2/x-1-4=0

We multiply all the terms by the denominator


(1.5x)*x-1*x-4*x-2=0

We add all the numbers together, and all the variables

(+1.5x)*x-1*x-4*x-2=0

We add all the numbers together, and all the variables

-5x+(+1.5x)*x-2=0

We multiply parentheses

x^2-5x-2=0

a = 1; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·1·(-2)
Δ = 33
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{-(-5)-\sqrt{33}}{2*1}=\frac{5-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*1}=\frac{5+\sqrt{33}}{2}
$