3-5/6x=2x+8

Solution for 3-5/6x=2x+8 equation:

3-5/6x=2x+8

We move all terms to the left:

3-5/6x-(2x+8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

-5/6x-2x-8+3=0

We multiply all the terms by the denominator


-2x*6x-8*6x+3*6x-5=0

Wy multiply elements

-12x^2-48x+18x-5=0

We add all the numbers together, and all the variables

-12x^2-30x-5=0

a = -12; b = -30; c = -5;
Δ = b2-4ac
Δ = -302-4·(-12)·(-5)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{165}}{2*-12}=\frac{30-2\sqrt{165}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{165}}{2*-12}=\frac{30+2\sqrt{165}}{-24}
$