0=x^2-14x-51

Solution for 0=x^2-14x-51 equation:

0=x^2-14x-51

We move all terms to the left:

0-(x^2-14x-51)=0

We add all the numbers together, and all the variables

-(x^2-14x-51)=0

We get rid of parentheses

-x^2+14x+51=0

We add all the numbers together, and all the variables

-1x^2+14x+51=0

a = -1; b = 14; c = +51;
Δ = b2-4ac
Δ = 142-4·(-1)·51
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{-(14)-20}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+20}{2*-1}=\frac{6}{-2}
=-3
$