1/6x-8/15=2/3x+3

Solution for 1/6x-8/15=2/3x+3 equation:

1/6x-8/15=2/3x+3

We move all terms to the left:

1/6x-8/15-(2/3x+3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

1/6x-2/3x-3-8/15=0

We calculate fractions


(-432x^2)/270x^2+45x/270x^2+(-180x)/270x^2-3=0

We multiply all the terms by the denominator


(-432x^2)+45x+(-180x)-3*270x^2=0

Wy multiply elements

(-432x^2)-810x^2+45x+(-180x)=0

We get rid of parentheses

-432x^2-810x^2+45x-180x=0

We add all the numbers together, and all the variables

-1242x^2-135x=0

a = -1242; b = -135; c = 0;
Δ = b2-4ac
Δ = -1352-4·(-1242)·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-135}{2*-1242}=\frac{0}{-2484}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+135}{2*-1242}=\frac{270}{-2484}
=-5/46
$