65=3x^2+4x+2

Solution for 65=3x^2+4x+2 equation:

65=3x^2+4x+2

We move all terms to the left:

65-(3x^2+4x+2)=0

We get rid of parentheses

-3x^2-4x-2+65=0

We add all the numbers together, and all the variables

-3x^2-4x+63=0

a = -3; b = -4; c = +63;
Δ = b2-4ac
Δ = -42-4·(-3)·63
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{193}}{2*-3}=\frac{4-2\sqrt{193}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{193}}{2*-3}=\frac{4+2\sqrt{193}}{-6}
$