13/6x-x=5

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

13/6x-x=5

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+13/6x-5=0

We multiply all the terms by the denominator


-1x*6x-5*6x+13=0

Wy multiply elements

-6x^2-30x+13=0

a = -6; b = -30; c = +13;
Δ = b2-4ac
Δ = -302-4·(-6)·13
Δ = 1212
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:

$\sqrt{\Delta}=\sqrt{1212}=\sqrt{4*303}=\sqrt{4}*\sqrt{303}=2\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{303}}{2*-6}=\frac{30-2\sqrt{303}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{303}}{2*-6}=\frac{30+2\sqrt{303}}{-12}
$