x^2+33x+270=810

Solution for x^2+33x+270=810 equation:

x^2+33x+270=810

We move all terms to the left:

x^2+33x+270-(810)=0

We add all the numbers together, and all the variables

x^2+33x-540=0

a = 1; b = 33; c = -540;
Δ = b2-4ac
Δ = 332-4·1·(-540)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-57}{2*1}=\frac{-90}{2}
=-45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+57}{2*1}=\frac{24}{2}
=12
$