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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


54x^2/72x^2+60x/72x^2+24x/72x^2=0

We multiply all the terms by the denominator


54x^2+60x+24x=0

We add all the numbers together, and all the variables

54x^2+84x=0

a = 54; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·54·0
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*54}=\frac{-168}{108}
=-1+5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*54}=\frac{0}{108}
=0
$