2x(x-4)=22

Solution for 2x(x-4)=22 equation:

2x(x-4)=22

We move all terms to the left:

2x(x-4)-(22)=0

We multiply parentheses

2x^2-8x-22=0

a = 2; b = -8; c = -22;
Δ = b2-4ac
Δ = -82-4·2·(-22)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*2}=\frac{8-4\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*2}=\frac{8+4\sqrt{15}}{4}
$