0=x^2+12x+29

Solution for 0=x^2+12x+29 equation:

0=x^2+12x+29

We move all terms to the left:

0-(x^2+12x+29)=0

We add all the numbers together, and all the variables

-(x^2+12x+29)=0

We get rid of parentheses

-x^2-12x-29=0

We add all the numbers together, and all the variables

-1x^2-12x-29=0

a = -1; b = -12; c = -29;
Δ = b2-4ac
Δ = -122-4·(-1)·(-29)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{7}}{2*-1}=\frac{12-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{7}}{2*-1}=\frac{12+2\sqrt{7}}{-2}
$