2x+288=x^2

Solution for 2x+288=x^2 equation:

2x+288=x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-x^2+2x+288=0

We add all the numbers together, and all the variables

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

a = -1; b = 2; c = +288;
Δ = b2-4ac
Δ = 22-4·(-1)·288
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*-1}=\frac{32}{-2}
=-16
$