x2+12x=33

Solution for x2+12x=33 equation:

x2+12x=33

We move all terms to the left:

x2+12x-(33)=0

We add all the numbers together, and all the variables

x^2+12x-33=0

a = 1; b = 12; c = -33;
Δ = b2-4ac
Δ = 122-4·1·(-33)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{69}}{2*1}=\frac{-12-2\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{69}}{2*1}=\frac{-12+2\sqrt{69}}{2}
$