X(x+12)=18.5

Solution for X(x+12)=18.5 equation:

X(X+12)=18.5

We move all terms to the left:

X(X+12)-(18.5)=0

We add all the numbers together, and all the variables

X(X+12)-18.5=0

We multiply parentheses

X^2+12X-18.5=0

a = 1; b = 12; c = -18.5;
Δ = b2-4ac
Δ = 122-4·1·(-18.5)
Δ = 218
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-\sqrt{218}}{2*1}=\frac{-12-\sqrt{218}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+\sqrt{218}}{2*1}=\frac{-12+\sqrt{218}}{2}
$