(4x-1)(2x+8)=0

Solution for (4x-1)(2x+8)=0 equation:

(4x-1)(2x+8)=0

We multiply parentheses ..

(+8x^2+32x-2x-8)=0

We get rid of parentheses

8x^2+32x-2x-8=0

We add all the numbers together, and all the variables

8x^2+30x-8=0

a = 8; b = 30; c = -8;
Δ = b2-4ac
Δ = 302-4·8·(-8)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-34}{2*8}=\frac{-64}{16}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+34}{2*8}=\frac{4}{16}
=1/4
$