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

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

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

We move all terms to the left:

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


Domain of the equation: 5x+15)!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

1/5x-3/x+15-3-5=0

We calculate fractions


x/5x^2+(-15x)/5x^2+15-3-5=0

We add all the numbers together, and all the variables

x/5x^2+(-15x)/5x^2+7=0

We multiply all the terms by the denominator


x+(-15x)+7*5x^2=0

Wy multiply elements

35x^2+x+(-15x)=0

We get rid of parentheses

35x^2+x-15x=0

We add all the numbers together, and all the variables

35x^2-14x=0

a = 35; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·35·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*35}=\frac{0}{70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*35}=\frac{28}{70}
=2/5
$