-2/3x+2=4x-6

Solution for -2/3x+2=4x-6 equation:

-2/3x+2=4x-6

We move all terms to the left:

-2/3x+2-(4x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-2/3x-4x+6+2=0

We multiply all the terms by the denominator


-4x*3x+6*3x+2*3x-2=0

Wy multiply elements

-12x^2+18x+6x-2=0

We add all the numbers together, and all the variables

-12x^2+24x-2=0

a = -12; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·(-12)·(-2)
Δ = 480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{30}}{2*-12}=\frac{-24-4\sqrt{30}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{30}}{2*-12}=\frac{-24+4\sqrt{30}}{-24}
$