5+6/x=13+2x

Solution for 5+6/x=13+2x equation:

5+6/x=13+2x

We move all terms to the left:

5+6/x-(13+2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6/x-(2x+13)+5=0

We get rid of parentheses

6/x-2x-13+5=0

We multiply all the terms by the denominator


-2x*x-13*x+5*x+6=0

We add all the numbers together, and all the variables

-8x-2x*x+6=0

Wy multiply elements

-2x^2-8x+6=0

a = -2; b = -8; c = +6;
Δ = b2-4ac
Δ = -82-4·(-2)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-2}=\frac{8-4\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-2}=\frac{8+4\sqrt{7}}{-4}
$