1/x+7=x+13

Solution for 1/x+7=x+13 equation:

1/x+7=x+13

We move all terms to the left:

1/x+7-(x+13)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

1/x-x-13+7=0

We multiply all the terms by the denominator


-x*x-13*x+7*x+1=0

We add all the numbers together, and all the variables

-6x-x*x+1=0

Wy multiply elements

-1x^2-6x+1=0

a = -1; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-1)·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{10}}{2*-1}=\frac{6-2\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{10}}{2*-1}=\frac{6+2\sqrt{10}}{-2}
$