3x*x-6*2+1+5/3=0

Solution for 3x*x-6*2+1+5/3=0 equation:

3x*x-6*2+1+5/3=0

We add all the numbers together, and all the variables

3x*x-11+5/3=0

Wy multiply elements

3x^2-11+5/3=0

We multiply all the terms by the denominator


3x^2*3+5-11*3=0

We add all the numbers together, and all the variables

3x^2*3-28=0

Wy multiply elements

9x^2-28=0

a = 9; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·9·(-28)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*9}=\frac{0-12\sqrt{7}}{18}
=-\frac{12\sqrt{7}}{18}
=-\frac{2\sqrt{7}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*9}=\frac{0+12\sqrt{7}}{18}
=\frac{12\sqrt{7}}{18}
=\frac{2\sqrt{7}}{3}
$