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

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

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

We move all terms to the left:

-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}
$