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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-4x^2+32x+x-8)=0

We get rid of parentheses

-4x^2+32x+x-8=0

We add all the numbers together, and all the variables

-4x^2+33x-8=0

a = -4; b = 33; c = -8;
Δ = b2-4ac
Δ = 332-4·(-4)·(-8)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-31}{2*-4}=\frac{-64}{-8}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+31}{2*-4}=\frac{-2}{-8}
=1/4
$