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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2+12x+1=0

a = 3; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·3·1
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{33}}{2*3}=\frac{-12-2\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{33}}{2*3}=\frac{-12+2\sqrt{33}}{6}
$