5/x-1-1.3x-1.3=-8

Solution for 5/x-1-1.3x-1.3=-8 equation:

5/x-1-1.3x-1.3=-8

We move all terms to the left:

5/x-1-1.3x-1.3-(-8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1.3x+5/x+5.7=0

We multiply all the terms by the denominator


-(1.3x)*x+(5.7)*x+5=0

We add all the numbers together, and all the variables

-(+1.3x)*x+(5.7)*x+5=0

We multiply parentheses

-x^2+5.7x+5=0

We add all the numbers together, and all the variables

-1x^2+5.7x+5=0

a = -1; b = 5.7; c = +5;
Δ = b2-4ac
Δ = 5.72-4·(-1)·5
Δ = 52.49
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{-(5.7)-\sqrt{52.49}}{2*-1}=\frac{-5.7-\sqrt{52.49}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.7)+\sqrt{52.49}}{2*-1}=\frac{-5.7+\sqrt{52.49}}{-2}
$