12-4x=x2+42x+441

Solution for 12-4x=x2+42x+441 equation:

12-4x=x2+42x+441

We move all terms to the left:

12-4x-(x2+42x+441)=0

We add all the numbers together, and all the variables

-(+x^2+42x+441)-4x+12=0

We get rid of parentheses

-x^2-42x-4x-441+12=0

We add all the numbers together, and all the variables

-1x^2-46x-429=0

a = -1; b = -46; c = -429;
Δ = b2-4ac
Δ = -462-4·(-1)·(-429)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-20}{2*-1}=\frac{26}{-2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+20}{2*-1}=\frac{66}{-2}
=-33
$