6-2x-(x^2+42x+441)=0

Solution for 6-2x-(x^2+42x+441)=0 equation:

6-2x-(x^2+42x+441)=0

We get rid of parentheses

-x^2-2x-42x-441+6=0

We add all the numbers together, and all the variables

-1x^2-44x-435=0

a = -1; b = -44; c = -435;
Δ = b2-4ac
Δ = -442-4·(-1)·(-435)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-14}{2*-1}=\frac{30}{-2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+14}{2*-1}=\frac{58}{-2}
=-29
$