X*(x+12)=493

Solution for X*(x+12)=493 equation:

X(X+12)=493

We move all terms to the left:

X(X+12)-(493)=0

We multiply parentheses

X^2+12X-493=0

a = 1; b = 12; c = -493;
Δ = b2-4ac
Δ = 122-4·1·(-493)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-46}{2*1}=\frac{-58}{2}
=-29
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+46}{2*1}=\frac{34}{2}
=17
$