0=x^2+4x-288

Solution for 0=x^2+4x-288 equation:

0=x^2+4x-288

We move all terms to the left:

0-(x^2+4x-288)=0

We add all the numbers together, and all the variables

-(x^2+4x-288)=0

We get rid of parentheses

-x^2-4x+288=0

We add all the numbers together, and all the variables

-1x^2-4x+288=0

a = -1; b = -4; c = +288;
Δ = b2-4ac
Δ = -42-4·(-1)·288
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{73}}{2*-1}=\frac{4-4\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{73}}{2*-1}=\frac{4+4\sqrt{73}}{-2}
$