0=x^2-12x-8

Solution for 0=x^2-12x-8 equation:

0=x^2-12x-8

We move all terms to the left:

0-(x^2-12x-8)=0

We add all the numbers together, and all the variables

-(x^2-12x-8)=0

We get rid of parentheses

-x^2+12x+8=0

We add all the numbers together, and all the variables

-1x^2+12x+8=0

a = -1; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·(-1)·8
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{11}}{2*-1}=\frac{-12-4\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{11}}{2*-1}=\frac{-12+4\sqrt{11}}{-2}
$