-2x+3x2=65

Solution for -2x+3x2=65 equation:

-2x+3x^2=65

We move all terms to the left:

-2x+3x^2-(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
$