22x-x^2-21=0

Solution for 22x-x^2-21=0 equation:

22x-x^2-21=0

We add all the numbers together, and all the variables

-1x^2+22x-21=0

a = -1; b = 22; c = -21;
Δ = b2-4ac
Δ = 222-4·(-1)·(-21)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-20}{2*-1}=\frac{-42}{-2}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+20}{2*-1}=\frac{-2}{-2}
=1
$