5/x-4/5x=58

Solution for 5/x-4/5x=58 equation:

5/x-4/5x=58

We move all terms to the left:

5/x-4/5x-(58)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


25x/5x^2+(-4x)/5x^2-58=0

We multiply all the terms by the denominator


25x+(-4x)-58*5x^2=0

Wy multiply elements

-290x^2+25x+(-4x)=0

We get rid of parentheses

-290x^2+25x-4x=0

We add all the numbers together, and all the variables

-290x^2+21x=0

a = -290; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-290)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-290}=\frac{-42}{-580}
=21/290
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-290}=\frac{0}{-580}
=0
$