5/6x-2+1/3x=1/2

Solution for 5/6x-2+1/3x=1/2 equation:

5/6x-2+1/3x=1/2

We move all terms to the left:

5/6x-2+1/3x-(1/2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x+1/3x-2-(+1/2)=0

We get rid of parentheses

5/6x+1/3x-2-1/2=0

We calculate fractions


(-54x^2)/72x^2+60x/72x^2+24x/72x^2-2=0

We multiply all the terms by the denominator


(-54x^2)+60x+24x-2*72x^2=0

We add all the numbers together, and all the variables

(-54x^2)+84x-2*72x^2=0

Wy multiply elements

(-54x^2)-144x^2+84x=0

We get rid of parentheses

-54x^2-144x^2+84x=0

We add all the numbers together, and all the variables

-198x^2+84x=0

a = -198; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-198)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-198}=\frac{-168}{-396}
=14/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-198}=\frac{0}{-396}
=0
$