5=-16x^2+6x+22

Solution for 5=-16x^2+6x+22 equation:

5=-16x^2+6x+22

We move all terms to the left:

5-(-16x^2+6x+22)=0

We get rid of parentheses

16x^2-6x-22+5=0

We add all the numbers together, and all the variables

16x^2-6x-17=0

a = 16; b = -6; c = -17;
Δ = b2-4ac
Δ = -62-4·16·(-17)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{281}}{2*16}=\frac{6-2\sqrt{281}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{281}}{2*16}=\frac{6+2\sqrt{281}}{32}
$