X^2=12x+288

Solution for X^2=12x+288 equation:

X^2=12X+288

We move all terms to the left:

X^2-(12X+288)=0

We get rid of parentheses

X^2-12X-288=0

a = 1; b = -12; c = -288;
Δ = b2-4ac
Δ = -122-4·1·(-288)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*1}=\frac{-24}{2}
=-12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*1}=\frac{48}{2}
=24
$