2/10x+13=x-107

Solution for 2/10x+13=x-107 equation:

2/10x+13=x-107

We move all terms to the left:

2/10x+13-(x-107)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

2/10x-x+107+13=0

We multiply all the terms by the denominator


-x*10x+107*10x+13*10x+2=0

Wy multiply elements

-10x^2+1070x+130x+2=0

We add all the numbers together, and all the variables

-10x^2+1200x+2=0

a = -10; b = 1200; c = +2;
Δ = b2-4ac
Δ = 12002-4·(-10)·2
Δ = 1440080
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:

$\sqrt{\Delta}=\sqrt{1440080}=\sqrt{16*90005}=\sqrt{16}*\sqrt{90005}=4\sqrt{90005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-4\sqrt{90005}}{2*-10}=\frac{-1200-4\sqrt{90005}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+4\sqrt{90005}}{2*-10}=\frac{-1200+4\sqrt{90005}}{-20}
$