5/6x-2=10+x

Solution for 5/6x-2=10+x equation:

5/6x-2=10+x

We move all terms to the left:

5/6x-2-(10+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

5/6x-(x+10)-2=0

We get rid of parentheses

5/6x-x-10-2=0

We multiply all the terms by the denominator


-x*6x-10*6x-2*6x+5=0

Wy multiply elements

-6x^2-60x-12x+5=0

We add all the numbers together, and all the variables

-6x^2-72x+5=0

a = -6; b = -72; c = +5;
Δ = b2-4ac
Δ = -722-4·(-6)·5
Δ = 5304
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:

$\sqrt{\Delta}=\sqrt{5304}=\sqrt{4*1326}=\sqrt{4}*\sqrt{1326}=2\sqrt{1326}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1326}}{2*-6}=\frac{72-2\sqrt{1326}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1326}}{2*-6}=\frac{72+2\sqrt{1326}}{-12}
$