x(8x+12)=8

Solution for x(8x+12)=8 equation:

x(8x+12)=8

We move all terms to the left:

x(8x+12)-(8)=0

We multiply parentheses

8x^2+12x-8=0

a = 8; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·8·(-8)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*8}=\frac{8}{16}
=1/2
$