2/x-4+8/5x+15=10

Solution for 2/x-4+8/5x+15=10 equation:

2/x-4+8/5x+15=10

We move all terms to the left:

2/x-4+8/5x+15-(10)=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

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

We calculate fractions


10x/5x^2+8x/5x^2+1=0

We multiply all the terms by the denominator


10x+8x+1*5x^2=0

We add all the numbers together, and all the variables

18x+1*5x^2=0

Wy multiply elements

5x^2+18x=0

a = 5; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·5·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*5}=\frac{-36}{10}
=-3+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*5}=\frac{0}{10}
=0
$