-1/5x-10=x+8

Solution for -1/5x-10=x+8 equation:

-1/5x-10=x+8

We move all terms to the left:

-1/5x-10-(x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-x-8-10=0

We multiply all the terms by the denominator


-x*5x-8*5x-10*5x-1=0

Wy multiply elements

-5x^2-40x-50x-1=0

We add all the numbers together, and all the variables

-5x^2-90x-1=0

a = -5; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·(-5)·(-1)
Δ = 8080
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:

$\sqrt{\Delta}=\sqrt{8080}=\sqrt{16*505}=\sqrt{16}*\sqrt{505}=4\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{505}}{2*-5}=\frac{90-4\sqrt{505}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{505}}{2*-5}=\frac{90+4\sqrt{505}}{-10}
$