2/3x-1=-x-6

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

2/3x-1=-x-6

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*3x+6*3x-1*3x+2=0

Wy multiply elements

3x^2+18x-3x+2=0

We add all the numbers together, and all the variables

3x^2+15x+2=0

a = 3; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·3·2
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{201}}{2*3}=\frac{-15-\sqrt{201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*3}=\frac{-15+\sqrt{201}}{6}
$