1/2x+13=x-107

Solution for 1/2x+13=x-107 equation:

1/2x+13=x-107

We move all terms to the left:

1/2x+13-(x-107)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x+107+13=0

We multiply all the terms by the denominator


-x*2x+107*2x+13*2x+1=0

Wy multiply elements

-2x^2+214x+26x+1=0

We add all the numbers together, and all the variables

-2x^2+240x+1=0

a = -2; b = 240; c = +1;
Δ = b2-4ac
Δ = 2402-4·(-2)·1
Δ = 57608
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:

$\sqrt{\Delta}=\sqrt{57608}=\sqrt{4*14402}=\sqrt{4}*\sqrt{14402}=2\sqrt{14402}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{14402}}{2*-2}=\frac{-240-2\sqrt{14402}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{14402}}{2*-2}=\frac{-240+2\sqrt{14402}}{-4}
$