(a-6)(3a-15)=0

Solution for (a-6)(3a-15)=0 equation:

(a-6)(3a-15)=0

We multiply parentheses ..

(+3a^2-15a-18a+90)=0

We get rid of parentheses

3a^2-15a-18a+90=0

We add all the numbers together, and all the variables

3a^2-33a+90=0

a = 3; b = -33; c = +90;
Δ = b2-4ac
Δ = -332-4·3·90
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*3}=\frac{30}{6}
=5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*3}=\frac{36}{6}
=6
$