441=x^2+30x+8

Solution for 441=x^2+30x+8 equation:

441=x^2+30x+8

We move all terms to the left:

441-(x^2+30x+8)=0

We get rid of parentheses

-x^2-30x-8+441=0

We add all the numbers together, and all the variables

-1x^2-30x+433=0

a = -1; b = -30; c = +433;
Δ = b2-4ac
Δ = -302-4·(-1)·433
Δ = 2632
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:

$\sqrt{\Delta}=\sqrt{2632}=\sqrt{4*658}=\sqrt{4}*\sqrt{658}=2\sqrt{658}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{658}}{2*-1}=\frac{30-2\sqrt{658}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{658}}{2*-1}=\frac{30+2\sqrt{658}}{-2}
$