5/6x+3=x

Solution for 5/6x+3=x equation:

5/6x+3=x

We move all terms to the left:

5/6x+3-(x)=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+5/6x+3=0

We multiply all the terms by the denominator


-1x*6x+3*6x+5=0

Wy multiply elements

-6x^2+18x+5=0

a = -6; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-6)·5
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{111}}{2*-6}=\frac{-18-2\sqrt{111}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{111}}{2*-6}=\frac{-18+2\sqrt{111}}{-12}
$