2(4x+1)(x+2)=0

Solution for 2(4x+1)(x+2)=0 equation:

2(4x+1)(x+2)=0

We multiply parentheses ..

2(+4x^2+8x+x+2)=0

We multiply parentheses

8x^2+16x+2x+4=0

We add all the numbers together, and all the variables

8x^2+18x+4=0

a = 8; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·8·4
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-14}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+14}{2*8}=\frac{-4}{16}
=-1/4
$