-3x^2-2x=-65

Solution for -3x^2-2x=-65 equation:

-3x^2-2x=-65

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -3; b = -2; c = +65;
Δ = b2-4ac
Δ = -22-4·(-3)·65
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-28}{2*-3}=\frac{-26}{-6}
=4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+28}{2*-3}=\frac{30}{-6}
=-5
$