-1/x+2=7/5x+10+1

Solution for -1/x+2=7/5x+10+1 equation:

-1/x+2=7/5x+10+1

We move all terms to the left:

-1/x+2-(7/5x+10+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+10+1)!=0

We move all terms containing x to the left, all other terms to the right

5x+1)!=-10

x∈R


We add all the numbers together, and all the variables

-1/x-(7/5x+11)+2=0

We get rid of parentheses

-1/x-7/5x-11+2=0

We calculate fractions


(-5x)/5x^2+(-7x)/5x^2-11+2=0

We add all the numbers together, and all the variables

(-5x)/5x^2+(-7x)/5x^2-9=0

We multiply all the terms by the denominator


(-5x)+(-7x)-9*5x^2=0

Wy multiply elements

-45x^2+(-5x)+(-7x)=0

We get rid of parentheses

-45x^2-5x-7x=0

We add all the numbers together, and all the variables

-45x^2-12x=0

a = -45; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-45)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-45}=\frac{24}{-90}
=-4/15
$