1/5x+13=x+107

Solution for 1/5x+13=x+107 equation:

1/5x+13=x+107

We move all terms to the left:

1/5x+13-(x+107)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x-107+13=0

We multiply all the terms by the denominator


-x*5x-107*5x+13*5x+1=0

Wy multiply elements

-5x^2-535x+65x+1=0

We add all the numbers together, and all the variables

-5x^2-470x+1=0

a = -5; b = -470; c = +1;
Δ = b2-4ac
Δ = -4702-4·(-5)·1
Δ = 220920
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:

$\sqrt{\Delta}=\sqrt{220920}=\sqrt{4*55230}=\sqrt{4}*\sqrt{55230}=2\sqrt{55230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-470)-2\sqrt{55230}}{2*-5}=\frac{470-2\sqrt{55230}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-470)+2\sqrt{55230}}{2*-5}=\frac{470+2\sqrt{55230}}{-10}
$