(5x-8)*(x-9)=0

Solution for (5x-8)*(x-9)=0 equation:

(5x-8)(x-9)=0

We multiply parentheses ..

(+5x^2-45x-8x+72)=0

We get rid of parentheses

5x^2-45x-8x+72=0

We add all the numbers together, and all the variables

5x^2-53x+72=0

a = 5; b = -53; c = +72;
Δ = b2-4ac
Δ = -532-4·5·72
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-37}{2*5}=\frac{16}{10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+37}{2*5}=\frac{90}{10}
=9
$