2/3x-2=2x-7

Solution for 2/3x-2=2x-7 equation:

2/3x-2=2x-7

We move all terms to the left:

2/3x-2-(2x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-2x+7-2=0

We multiply all the terms by the denominator


-2x*3x+7*3x-2*3x+2=0

Wy multiply elements

-6x^2+21x-6x+2=0

We add all the numbers together, and all the variables

-6x^2+15x+2=0

a = -6; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-6)·2
Δ = 273
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{273}}{2*-6}=\frac{-15-\sqrt{273}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*-6}=\frac{-15+\sqrt{273}}{-12}
$