-2/x=-5-5x

Solution for -2/x=-5-5x equation:

-2/x=-5-5x

We move all terms to the left:

-2/x-(-5-5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2/x-(-5x-5)=0

We get rid of parentheses

-2/x+5x+5=0

We multiply all the terms by the denominator


5x*x+5*x-2=0

We add all the numbers together, and all the variables

5x+5x*x-2=0

Wy multiply elements

5x^2+5x-2=0

a = 5; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·5·(-2)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{65}}{2*5}=\frac{-5-\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*5}=\frac{-5+\sqrt{65}}{10}
$