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

Solution for 1/x+2=-5/8x-5 equation:

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

We move all terms to the left:

1/x+2-(-5/8x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

8x/8x^2+5x/8x^2+7=0

We multiply all the terms by the denominator


8x+5x+7*8x^2=0

We add all the numbers together, and all the variables

13x+7*8x^2=0

Wy multiply elements

56x^2+13x=0

a = 56; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·56·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*56}=\frac{-26}{112}
=-13/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*56}=\frac{0}{112}
=0
$