(2+x)x=4/3

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

(2+x)x=4/3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+6x-4=0

a = 3; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·3·(-4)
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*3}=\frac{-6-2\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*3}=\frac{-6+2\sqrt{21}}{6}
$