3(x-3)(5-x)=0

Solution for 3(x-3)(5-x)=0 equation:

3(x-3)(5-x)=0

We add all the numbers together, and all the variables

3(x-3)(-1x+5)=0

We multiply parentheses ..

3(-1x^2+5x+3x-15)=0

We multiply parentheses

-3x^2+15x+9x-45=0

We add all the numbers together, and all the variables

-3x^2+24x-45=0

a = -3; b = 24; c = -45;
Δ = b2-4ac
Δ = 242-4·(-3)·(-45)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6}{2*-3}=\frac{-18}{-6}
=+3
$