-5=-16x^2+22x

Solution for -5=-16x^2+22x equation:

-5=-16x^2+22x

We move all terms to the left:

-5-(-16x^2+22x)=0

We get rid of parentheses

16x^2-22x-5=0

a = 16; b = -22; c = -5;
Δ = b2-4ac
Δ = -222-4·16·(-5)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{201}}{2*16}=\frac{22-2\sqrt{201}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{201}}{2*16}=\frac{22+2\sqrt{201}}{32}
$