-1/5x-15=x+9

Solution for -1/5x-15=x+9 equation:

-1/5x-15=x+9

We move all terms to the left:

-1/5x-15-(x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-x-9-15=0

We multiply all the terms by the denominator


-x*5x-9*5x-15*5x-1=0

Wy multiply elements

-5x^2-45x-75x-1=0

We add all the numbers together, and all the variables

-5x^2-120x-1=0

a = -5; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·(-5)·(-1)
Δ = 14380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14380}=\sqrt{4*3595}=\sqrt{4}*\sqrt{3595}=2\sqrt{3595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3595}}{2*-5}=\frac{120-2\sqrt{3595}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3595}}{2*-5}=\frac{120+2\sqrt{3595}}{-10}
$