-1/5x-40=-x+8

Solution for -1/5x-40=-x+8 equation:

-1/5x-40=-x+8

We move all terms to the left:

-1/5x-40-(-x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1/5x-(-1x+8)-40=0

We get rid of parentheses

-1/5x+1x-8-40=0

We multiply all the terms by the denominator


1x*5x-8*5x-40*5x-1=0

Wy multiply elements

5x^2-40x-200x-1=0

We add all the numbers together, and all the variables

5x^2-240x-1=0

a = 5; b = -240; c = -1;
Δ = b2-4ac
Δ = -2402-4·5·(-1)
Δ = 57620
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:

$\sqrt{\Delta}=\sqrt{57620}=\sqrt{4*14405}=\sqrt{4}*\sqrt{14405}=2\sqrt{14405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14405}}{2*5}=\frac{240-2\sqrt{14405}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14405}}{2*5}=\frac{240+2\sqrt{14405}}{10}
$