X^2+12x=492

Solution for X^2+12x=492 equation:

X^2+12X=492

We move all terms to the left:

X^2+12X-(492)=0

a = 1; b = 12; c = -492;
Δ = b2-4ac
Δ = 122-4·1·(-492)
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{33}}{2*1}=\frac{-12-8\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{33}}{2*1}=\frac{-12+8\sqrt{33}}{2}
$