0=x^2+420x+40500

Solution for 0=x^2+420x+40500 equation:

0=x^2+420x+40500

We move all terms to the left:

0-(x^2+420x+40500)=0

We add all the numbers together, and all the variables

-(x^2+420x+40500)=0

We get rid of parentheses

-x^2-420x-40500=0

We add all the numbers together, and all the variables

-1x^2-420x-40500=0

a = -1; b = -420; c = -40500;
Δ = b2-4ac
Δ = -4202-4·(-1)·(-40500)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-120}{2*-1}=\frac{300}{-2}
=-150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+120}{2*-1}=\frac{540}{-2}
=-270
$