-459x^2-3x+2=0

Solution for -459x^2-3x+2=0 equation:

-459x^2-3x+2=0

a = -459; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-459)·2
Δ = 3681
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:

$\sqrt{\Delta}=\sqrt{3681}=\sqrt{9*409}=\sqrt{9}*\sqrt{409}=3\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{409}}{2*-459}=\frac{3-3\sqrt{409}}{-918}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{409}}{2*-459}=\frac{3+3\sqrt{409}}{-918}
$