0=x^2+16x-144

Solution for 0=x^2+16x-144 equation:

0=x^2+16x-144

We move all terms to the left:

0-(x^2+16x-144)=0

We add all the numbers together, and all the variables

-(x^2+16x-144)=0

We get rid of parentheses

-x^2-16x+144=0

We add all the numbers together, and all the variables

-1x^2-16x+144=0

a = -1; b = -16; c = +144;
Δ = b2-4ac
Δ = -162-4·(-1)·144
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{13}}{2*-1}=\frac{16-8\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{13}}{2*-1}=\frac{16+8\sqrt{13}}{-2}
$