2/5x-6/x=1

Solution for 2/5x-6/x=1 equation:

2/5x-6/x=1

We move all terms to the left:

2/5x-6/x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


2x/5x^2+(-30x)/5x^2-1=0

We multiply all the terms by the denominator


2x+(-30x)-1*5x^2=0

Wy multiply elements

-5x^2+2x+(-30x)=0

We get rid of parentheses

-5x^2+2x-30x=0

We add all the numbers together, and all the variables

-5x^2-28x=0

a = -5; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-5)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-5}=\frac{56}{-10}
=-5+3/5
$