4/3x-2x=-6

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

4/3x-2x=-6

We move all terms to the left:

4/3x-2x-(-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

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+18x+4=0

a = -6; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·(-6)·4
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*-6}=\frac{-18-2\sqrt{105}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*-6}=\frac{-18+2\sqrt{105}}{-12}
$