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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-8x^2+16x-12x+24)=0

We get rid of parentheses

-8x^2+16x-12x+24=0

We add all the numbers together, and all the variables

-8x^2+4x+24=0

a = -8; b = 4; c = +24;
Δ = b2-4ac
Δ = 42-4·(-8)·24
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*-8}=\frac{-32}{-16}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*-8}=\frac{24}{-16}
=-1+1/2
$