484=x(x+33)

Solution for 484=x(x+33) equation:

484=x(x+33)

We move all terms to the left:

484-(x(x+33))=0


We calculate terms in parentheses: -(x(x+33)), so:

x(x+33)

We multiply parentheses

x^2+33x

Back to the equation:

-(x^2+33x)


We get rid of parentheses

-x^2-33x+484=0

We add all the numbers together, and all the variables

-1x^2-33x+484=0

a = -1; b = -33; c = +484;
Δ = b2-4ac
Δ = -332-4·(-1)·484
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-55}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+55}{2*-1}=\frac{88}{-2}
=-44
$