(-5a+8)(-3a+9)=0

Solution for (-5a+8)(-3a+9)=0 equation:

(-5a+8)(-3a+9)=0

We multiply parentheses ..

(+15a^2-45a-24a+72)=0

We get rid of parentheses

15a^2-45a-24a+72=0

We add all the numbers together, and all the variables

15a^2-69a+72=0

a = 15; b = -69; c = +72;
Δ = b2-4ac
Δ = -692-4·15·72
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-21}{2*15}=\frac{48}{30}
=1+3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+21}{2*15}=\frac{90}{30}
=3
$