1/5x+12=x-107

Solution for 1/5x+12=x-107 equation:

1/5x+12=x-107

We move all terms to the left:

1/5x+12-(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+12=0

We multiply all the terms by the denominator


-x*5x+107*5x+12*5x+1=0

Wy multiply elements

-5x^2+535x+60x+1=0

We add all the numbers together, and all the variables

-5x^2+595x+1=0

a = -5; b = 595; c = +1;
Δ = b2-4ac
Δ = 5952-4·(-5)·1
Δ = 354045
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(595)-\sqrt{354045}}{2*-5}=\frac{-595-\sqrt{354045}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(595)+\sqrt{354045}}{2*-5}=\frac{-595+\sqrt{354045}}{-10}
$