1/5x+13=x-27

Solution for 1/5x+13=x-27 equation:

1/5x+13=x-27

We move all terms to the left:

1/5x+13-(x-27)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+27+13=0

We multiply all the terms by the denominator


-x*5x+27*5x+13*5x+1=0

Wy multiply elements

-5x^2+135x+65x+1=0

We add all the numbers together, and all the variables

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

a = -5; b = 200; c = +1;
Δ = b2-4ac
Δ = 2002-4·(-5)·1
Δ = 40020
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:

$\sqrt{\Delta}=\sqrt{40020}=\sqrt{4*10005}=\sqrt{4}*\sqrt{10005}=2\sqrt{10005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{10005}}{2*-5}=\frac{-200-2\sqrt{10005}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{10005}}{2*-5}=\frac{-200+2\sqrt{10005}}{-10}
$