X^2+12x-333=0

Solution for X^2+12x-333=0 equation:

X^2+12X-333=0

a = 1; b = 12; c = -333;
Δ = b2-4ac
Δ = 122-4·1·(-333)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{41}}{2*1}=\frac{-12-6\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{41}}{2*1}=\frac{-12+6\sqrt{41}}{2}
$