22=80x-16x^2

Solution for 22=80x-16x^2 equation:

22=80x-16x^2

We move all terms to the left:

22-(80x-16x^2)=0

We get rid of parentheses

16x^2-80x+22=0

a = 16; b = -80; c = +22;
Δ = b2-4ac
Δ = -802-4·16·22
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{78}}{2*16}=\frac{80-8\sqrt{78}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{78}}{2*16}=\frac{80+8\sqrt{78}}{32}
$