(5a-9)(a+6)=0

Solution for (5a-9)(a+6)=0 equation:

(5a-9)(a+6)=0

We multiply parentheses ..

(+5a^2+30a-9a-54)=0

We get rid of parentheses

5a^2+30a-9a-54=0

We add all the numbers together, and all the variables

5a^2+21a-54=0

a = 5; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·5·(-54)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-39}{2*5}=\frac{-60}{10}
=-6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+39}{2*5}=\frac{18}{10}
=1+4/5
$