(15x+30)/(-5x-10)=x

Solution for (15x+30)/(-5x-10)=x equation:

(15x+30)/(-5x-10)=x

We move all terms to the left:

(15x+30)/(-5x-10)-(x)=0


Domain of the equation: (-5x-10)!=0

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

-5x!=10

x!=10/-5

x!=-2

x∈R


We add all the numbers together, and all the variables

-1x+(15x+30)/(-5x-10)=0

We multiply all the terms by the denominator


-1x*(-5x-10)+(15x+30)=0

We multiply parentheses

5x^2+10x+(15x+30)=0

We get rid of parentheses

5x^2+10x+15x+30=0

We add all the numbers together, and all the variables

5x^2+25x+30=0

a = 5; b = 25; c = +30;
Δ = b2-4ac
Δ = 252-4·5·30
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5}{2*5}=\frac{-20}{10}
=-2
$