33=x(23-2x/2)

Solution for 33=x(23-2x/2) equation:

33=x(23-2x/2)

We move all terms to the left:

33-(x(23-2x/2))=0

We add all the numbers together, and all the variables

-(x(-2x/2+23))+33=0

We multiply all the terms by the denominator


-(x(-2x+33*2+23))=0


We calculate terms in parentheses: -(x(-2x+33*2+23)), so:

x(-2x+33*2+23)

We add all the numbers together, and all the variables

x(-2x+89)

We multiply parentheses

-2x^2+89x

Back to the equation:

-(-2x^2+89x)


We get rid of parentheses

2x^2-89x=0

a = 2; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·2·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*2}=\frac{178}{4}
=44+1/2
$