0=x2+14x-64

Solution for 0=x2+14x-64 equation:

0=x2+14x-64

We move all terms to the left:

0-(x2+14x-64)=0

We add all the numbers together, and all the variables

-(+x^2+14x-64)+0=0

We add all the numbers together, and all the variables

-(+x^2+14x-64)=0

We get rid of parentheses

-x^2-14x+64=0

We add all the numbers together, and all the variables

-1x^2-14x+64=0

a = -1; b = -14; c = +64;
Δ = b2-4ac
Δ = -142-4·(-1)·64
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{113}}{2*-1}=\frac{14-2\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{113}}{2*-1}=\frac{14+2\sqrt{113}}{-2}
$