0=x^2+12x-69

Solution for 0=x^2+12x-69 equation:

0=x^2+12x-69

We move all terms to the left:

0-(x^2+12x-69)=0

We add all the numbers together, and all the variables

-(x^2+12x-69)=0

We get rid of parentheses

-x^2-12x+69=0

We add all the numbers together, and all the variables

-1x^2-12x+69=0

a = -1; b = -12; c = +69;
Δ = b2-4ac
Δ = -122-4·(-1)·69
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{105}}{2*-1}=\frac{12-2\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{105}}{2*-1}=\frac{12+2\sqrt{105}}{-2}
$