2x(4x+8)=22

Solution for 2x(4x+8)=22 equation:

2x(4x+8)=22

We move all terms to the left:

2x(4x+8)-(22)=0

We multiply parentheses

8x^2+16x-22=0

a = 8; b = 16; c = -22;
Δ = b2-4ac
Δ = 162-4·8·(-22)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{15}}{2*8}=\frac{-16-8\sqrt{15}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{15}}{2*8}=\frac{-16+8\sqrt{15}}{16}
$