-1/5x-18=2-x

Solution for -1/5x-18=2-x equation:

-1/5x-18=2-x

We move all terms to the left:

-1/5x-18-(2-x)=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+2)-18=0

We get rid of parentheses

-1/5x+1x-2-18=0

We multiply all the terms by the denominator


1x*5x-2*5x-18*5x-1=0

Wy multiply elements

5x^2-10x-90x-1=0

We add all the numbers together, and all the variables

5x^2-100x-1=0

a = 5; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·5·(-1)
Δ = 10020
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:

$\sqrt{\Delta}=\sqrt{10020}=\sqrt{4*2505}=\sqrt{4}*\sqrt{2505}=2\sqrt{2505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2505}}{2*5}=\frac{100-2\sqrt{2505}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2505}}{2*5}=\frac{100+2\sqrt{2505}}{10}
$