X(0.50)-(30-x)(x)=33

Solution for X(0.50)-(30-x)(x)=33 equation:

X(0.50)-(30-X)(X)=33

We move all terms to the left:

X(0.50)-(30-X)(X)-(33)=0

We add all the numbers together, and all the variables

X(0.5)-(-1X+30)X-33=0

We multiply parentheses

1X^2+0.5X-30X-33=0

We add all the numbers together, and all the variables

X^2-29.5X-33=0

a = 1; b = -29.5; c = -33;
Δ = b2-4ac
Δ = -29.52-4·1·(-33)
Δ = 1002.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29.5)-\sqrt{1002.25}}{2*1}=\frac{29.5-\sqrt{1002.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29.5)+\sqrt{1002.25}}{2*1}=\frac{29.5+\sqrt{1002.25}}{2}
$