1/x-16/5x-3=-1

Solution for 1/x-16/5x-3=-1 equation:

1/x-16/5x-3=-1

We move all terms to the left:

1/x-16/5x-3-(-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/x-16/5x-2=0

We calculate fractions


5x/5x^2+(-16x)/5x^2-2=0

We multiply all the terms by the denominator


5x+(-16x)-2*5x^2=0

Wy multiply elements

-10x^2+5x+(-16x)=0

We get rid of parentheses

-10x^2+5x-16x=0

We add all the numbers together, and all the variables

-10x^2-11x=0

a = -10; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-10)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-10}=\frac{22}{-20}
=-1+1/10
$