3x^2+x=2/3

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

3x^2+x=2/3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2+3x-2=0

a = 9; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·9·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*9}=\frac{6}{18}
=1/3
$