232=2x(33-2x)

Solution for 232=2x(33-2x) equation:

232=2x(33-2x)

We move all terms to the left:

232-(2x(33-2x))=0

We add all the numbers together, and all the variables

-(2x(-2x+33))+232=0


We calculate terms in parentheses: -(2x(-2x+33)), so:

2x(-2x+33)

We multiply parentheses

-4x^2+66x

Back to the equation:

-(-4x^2+66x)


We get rid of parentheses

4x^2-66x+232=0

a = 4; b = -66; c = +232;
Δ = b2-4ac
Δ = -662-4·4·232
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{161}}{2*4}=\frac{66-2\sqrt{161}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{161}}{2*4}=\frac{66+2\sqrt{161}}{8}
$