0=x^2-8x-51

Solution for 0=x^2-8x-51 equation:

0=x^2-8x-51

We move all terms to the left:

0-(x^2-8x-51)=0

We add all the numbers together, and all the variables

-(x^2-8x-51)=0

We get rid of parentheses

-x^2+8x+51=0

We add all the numbers together, and all the variables

-1x^2+8x+51=0

a = -1; b = 8; c = +51;
Δ = b2-4ac
Δ = 82-4·(-1)·51
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{67}}{2*-1}=\frac{-8-2\sqrt{67}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{67}}{2*-1}=\frac{-8+2\sqrt{67}}{-2}
$