(-2x-10)/(x+7)=3/x

Solution for (-2x-10)/(x+7)=3/x equation:

(-2x-10)/(x+7)=3/x

We move all terms to the left:

(-2x-10)/(x+7)-(3/x)=0


Domain of the equation: (x+7)!=0

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

x!=-7

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-2x-10)/(x+7)-(+3/x)=0

We get rid of parentheses

(-2x-10)/(x+7)-3/x=0

We calculate fractions


(-2x^2-10x)/(x^2+7x)+(-3x-21)/(x^2+7x)=0

We multiply all the terms by the denominator


(-2x^2-10x)+(-3x-21)=0

We get rid of parentheses

-2x^2-10x-3x-21=0

We add all the numbers together, and all the variables

-2x^2-13x-21=0

a = -2; b = -13; c = -21;
Δ = b2-4ac
Δ = -132-4·(-2)·(-21)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*-2}=\frac{12}{-4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*-2}=\frac{14}{-4}
=-3+1/2
$