x^2+33x+126=0

Solution for x^2+33x+126=0 equation:

x^2+33x+126=0

a = 1; b = 33; c = +126;
Δ = b2-4ac
Δ = 332-4·1·126
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{65}}{2*1}=\frac{-33-3\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{65}}{2*1}=\frac{-33+3\sqrt{65}}{2}
$