8/5x+2-1/x-7=0

Solution for 8/5x+2-1/x-7=0 equation:

8/5x+2-1/x-7=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

8/5x-1/x-5=0

We calculate fractions


8x/5x^2+(-5x)/5x^2-5=0

We multiply all the terms by the denominator


8x+(-5x)-5*5x^2=0

Wy multiply elements

-25x^2+8x+(-5x)=0

We get rid of parentheses

-25x^2+8x-5x=0

We add all the numbers together, and all the variables

-25x^2+3x=0

a = -25; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-25)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-25}=\frac{-6}{-50}
=3/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-25}=\frac{0}{-50}
=0
$