2/3x-10/3+1/2x=-1

Solution for 2/3x-10/3+1/2x=-1 equation:

2/3x-10/3+1/2x=-1

We move all terms to the left:

2/3x-10/3+1/2x-(-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+1/2x+1-10/3=0

We calculate fractions


4x/54x^2+27x/54x^2+(-20x)/54x^2+1=0

We multiply all the terms by the denominator


4x+27x+(-20x)+1*54x^2=0

We add all the numbers together, and all the variables

31x+(-20x)+1*54x^2=0

Wy multiply elements

54x^2+31x+(-20x)=0

We get rid of parentheses

54x^2+31x-20x=0

We add all the numbers together, and all the variables

54x^2+11x=0

a = 54; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·54·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*54}=\frac{-22}{108}
=-11/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*54}=\frac{0}{108}
=0
$