2x^2-16x=-22

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

2x^2-16x=-22

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2-16x+22=0

a = 2; b = -16; c = +22;
Δ = b2-4ac
Δ = -162-4·2·22
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{5}}{2*2}=\frac{16-4\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{5}}{2*2}=\frac{16+4\sqrt{5}}{4}
$