(4x-1)(9-x)=0

Solution for (4x-1)(9-x)=0 equation:

(4x-1)(9-x)=0

We add all the numbers together, and all the variables

(4x-1)(-1x+9)=0

We multiply parentheses ..

(-4x^2+36x+x-9)=0

We get rid of parentheses

-4x^2+36x+x-9=0

We add all the numbers together, and all the variables

-4x^2+37x-9=0

a = -4; b = 37; c = -9;
Δ = b2-4ac
Δ = 372-4·(-4)·(-9)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-35}{2*-4}=\frac{-72}{-8}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+35}{2*-4}=\frac{-2}{-8}
=1/4
$