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

Solution for X^2+3x-2/3=0 equation:

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

We multiply all the terms by the denominator


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

Wy multiply elements

3X^2+9X-2=0

a = 3; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·3·(-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{-(9)-\sqrt{105}}{2*3}=\frac{-9-\sqrt{105}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*3}=\frac{-9+\sqrt{105}}{6}
$