5/6x=x+13

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

5/6x=x+13

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-x-13=0

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2-78x+5=0

a = -6; b = -78; c = +5;
Δ = b2-4ac
Δ = -782-4·(-6)·5
Δ = 6204
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:

$\sqrt{\Delta}=\sqrt{6204}=\sqrt{4*1551}=\sqrt{4}*\sqrt{1551}=2\sqrt{1551}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1551}}{2*-6}=\frac{78-2\sqrt{1551}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1551}}{2*-6}=\frac{78+2\sqrt{1551}}{-12}
$