8(x+2)x=6

Solution for 8(x+2)x=6 equation:

8(x+2)x=6

We move all terms to the left:

8(x+2)x-(6)=0

We multiply parentheses

8x^2+16x-6=0

a = 8; b = 16; c = -6;
Δ = b2-4ac
Δ = 162-4·8·(-6)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{7}}{2*8}=\frac{-16-8\sqrt{7}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{7}}{2*8}=\frac{-16+8\sqrt{7}}{16}
$