-2x2+12x+16=22

Solution for -2x2+12x+16=22 equation:

-2x^2+12x+16=22

We move all terms to the left:

-2x^2+12x+16-(22)=0

We add all the numbers together, and all the variables

-2x^2+12x-6=0

a = -2; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·(-2)·(-6)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*-2}=\frac{-12-4\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*-2}=\frac{-12+4\sqrt{6}}{-4}
$