5/x+5=-3/5x

Solution for 5/x+5=-3/5x equation:

5/x+5=-3/5x

We move all terms to the left:

5/x+5-(-3/5x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

5/x+3/5x+5=0

We calculate fractions


25x/5x^2+3x/5x^2+5=0

We multiply all the terms by the denominator


25x+3x+5*5x^2=0

We add all the numbers together, and all the variables

28x+5*5x^2=0

Wy multiply elements

25x^2+28x=0

a = 25; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·25·0
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*25}=\frac{-56}{50}
=-1+3/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*25}=\frac{0}{50}
=0
$