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 get rid of parentheses

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

We multiply all the terms by the denominator


-x*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 = 249
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{249}}{2*-3}=\frac{-15-\sqrt{249}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*-3}=\frac{-15+\sqrt{249}}{-6}
$