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

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

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

We multiply parentheses ..

(+8x^2-72x-9x+81)=0

We get rid of parentheses

8x^2-72x-9x+81=0

We add all the numbers together, and all the variables

8x^2-81x+81=0

a = 8; b = -81; c = +81;
Δ = b2-4ac
Δ = -812-4·8·81
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-63}{2*8}=\frac{18}{16}
=1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+63}{2*8}=\frac{144}{16}
=9
$