(4x+3)(2x-8)=0

Solution for (4x+3)(2x-8)=0 equation:

(4x+3)(2x-8)=0

We multiply parentheses ..

(+8x^2-32x+6x-24)=0

We get rid of parentheses

8x^2-32x+6x-24=0

We add all the numbers together, and all the variables

8x^2-26x-24=0

a = 8; b = -26; c = -24;
Δ = b2-4ac
Δ = -262-4·8·(-24)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-38}{2*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+38}{2*8}=\frac{64}{16}
=4
$