2/x+1+5/5x+5=13

Solution for 2/x+1+5/5x+5=13 equation:

2/x+1+5/5x+5=13

We move all terms to the left:

2/x+1+5/5x+5-(13)=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+5/5x-7=0

We calculate fractions


10x/5x^2+5x/5x^2-7=0

We multiply all the terms by the denominator


10x+5x-7*5x^2=0

We add all the numbers together, and all the variables

15x-7*5x^2=0

Wy multiply elements

-35x^2+15x=0

a = -35; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-35)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-35}=\frac{-30}{-70}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-35}=\frac{0}{-70}
=0
$