2/3x+1=4x

Solution for 2/3x+1=4x equation:

2/3x+1=4x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+3x+2=0

a = -12; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-12)·2
Δ = 105
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{-(3)-\sqrt{105}}{2*-12}=\frac{-3-\sqrt{105}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-12}=\frac{-3+\sqrt{105}}{-24}
$