4/5x+15-1/x+3=3/5

Solution for 4/5x+15-1/x+3=3/5 equation:

4/5x+15-1/x+3=3/5

We move all terms to the left:

4/5x+15-1/x+3-(3/5)=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

4/5x-1/x+15+3-(+3/5)=0

We add all the numbers together, and all the variables

4/5x-1/x+18-(+3/5)=0

We get rid of parentheses

4/5x-1/x+18-3/5=0

We calculate fractions


4x/125x^2+(-125x)/125x^2+(-3x)/125x^2+18=0

We multiply all the terms by the denominator


4x+(-125x)+(-3x)+18*125x^2=0

Wy multiply elements

2250x^2+4x+(-125x)+(-3x)=0

We get rid of parentheses

2250x^2+4x-125x-3x=0

We add all the numbers together, and all the variables

2250x^2-124x=0

a = 2250; b = -124; c = 0;
Δ = b2-4ac
Δ = -1242-4·2250·0
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-124}{2*2250}=\frac{0}{4500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+124}{2*2250}=\frac{248}{4500}
=62/1125
$