x(2x+1)=4/3

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

x(2x+1)=4/3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+3x-4=0

a = 6; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·6·(-4)
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*6}=\frac{-3-\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*6}=\frac{-3+\sqrt{105}}{12}
$