(2x-9)(8-x)=0

Solution for (2x-9)(8-x)=0 equation:

(2x-9)(8-x)=0

We add all the numbers together, and all the variables

(2x-9)(-1x+8)=0

We multiply parentheses ..

(-2x^2+16x+9x-72)=0

We get rid of parentheses

-2x^2+16x+9x-72=0

We add all the numbers together, and all the variables

-2x^2+25x-72=0

a = -2; b = 25; c = -72;
Δ = b2-4ac
Δ = 252-4·(-2)·(-72)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7}{2*-2}=\frac{-18}{-4}
=4+1/2
$