22x-x^2=121/2

Solution for 22x-x^2=121/2 equation:

22x-x^2=121/2

We move all terms to the left:

22x-x^2-(121/2)=0

We add all the numbers together, and all the variables

-x^2+22x-(+121/2)=0

We add all the numbers together, and all the variables

-1x^2+22x-(+121/2)=0

We get rid of parentheses

-1x^2+22x-121/2=0

We multiply all the terms by the denominator


-1x^2*2+22x*2-121=0

Wy multiply elements

-2x^2+44x-121=0

a = -2; b = 44; c = -121;
Δ = b2-4ac
Δ = 442-4·(-2)·(-121)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-22\sqrt{2}}{2*-2}=\frac{-44-22\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+22\sqrt{2}}{2*-2}=\frac{-44+22\sqrt{2}}{-4}
$