2x-(4/3)x=-1/3

Solution for 2x-(4/3)x=-1/3 equation:

2x-(4/3)x=-1/3

We move all terms to the left:

2x-(4/3)x-(-1/3)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4/3)x-(-1/3)=0

We multiply parentheses

-4x^2+2x-(-1/3)=0

We get rid of parentheses

-4x^2+2x+1/3=0

We multiply all the terms by the denominator


-4x^2*3+2x*3+1=0

Wy multiply elements

-12x^2+6x+1=0

a = -12; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-12)·1
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-12}=\frac{-6-2\sqrt{21}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-12}=\frac{-6+2\sqrt{21}}{-24}
$