204-22x/2=x^2

Solution for 204-22x/2=x^2 equation:

204-22x/2=x^2

We move all terms to the left:

204-22x/2-(x^2)=0

determiningTheFunctionDomain
-x^2-22x/2+204=0

We add all the numbers together, and all the variables

-1x^2-22x/2+204=0

We multiply all the terms by the denominator


-1x^2*2-22x+204*2=0

We add all the numbers together, and all the variables

-1x^2*2-22x+408=0

Wy multiply elements

-2x^2-22x+408=0

a = -2; b = -22; c = +408;
Δ = b2-4ac
Δ = -222-4·(-2)·408
Δ = 3748
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:

$\sqrt{\Delta}=\sqrt{3748}=\sqrt{4*937}=\sqrt{4}*\sqrt{937}=2\sqrt{937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{937}}{2*-2}=\frac{22-2\sqrt{937}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{937}}{2*-2}=\frac{22+2\sqrt{937}}{-4}
$