-3x^2-x+420=0

Solution for -3x^2-x+420=0 equation:

-3x^2-x+420=0

We add all the numbers together, and all the variables

-3x^2-1x+420=0

a = -3; b = -1; c = +420;
Δ = b2-4ac
Δ = -12-4·(-3)·420
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-71}{2*-3}=\frac{-70}{-6}
=11+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+71}{2*-3}=\frac{72}{-6}
=-12
$