8-5/6x=-6-3x

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

8-5/6x=-6-3x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

18x^2+36x+48x-5=0

We add all the numbers together, and all the variables

18x^2+84x-5=0

a = 18; b = 84; c = -5;
Δ = b2-4ac
Δ = 842-4·18·(-5)
Δ = 7416
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:

$\sqrt{\Delta}=\sqrt{7416}=\sqrt{36*206}=\sqrt{36}*\sqrt{206}=6\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-6\sqrt{206}}{2*18}=\frac{-84-6\sqrt{206}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+6\sqrt{206}}{2*18}=\frac{-84+6\sqrt{206}}{36}
$