0=x^2-18x-420

Solution for 0=x^2-18x-420 equation:

0=x^2-18x-420

We move all terms to the left:

0-(x^2-18x-420)=0

We add all the numbers together, and all the variables

-(x^2-18x-420)=0

We get rid of parentheses

-x^2+18x+420=0

We add all the numbers together, and all the variables

-1x^2+18x+420=0

a = -1; b = 18; c = +420;
Δ = b2-4ac
Δ = 182-4·(-1)·420
Δ = 2004
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:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{501}}{2*-1}=\frac{-18-2\sqrt{501}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{501}}{2*-1}=\frac{-18+2\sqrt{501}}{-2}
$