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

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

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

We multiply parentheses ..

(+4x^2-16x-18x+72)=0

We get rid of parentheses

4x^2-16x-18x+72=0

We add all the numbers together, and all the variables

4x^2-34x+72=0

a = 4; b = -34; c = +72;
Δ = b2-4ac
Δ = -342-4·4·72
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*4}=\frac{32}{8}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*4}=\frac{36}{8}
=4+1/2
$