5(x-3)(x-6)=0

Solution for 5(x-3)(x-6)=0 equation:

5(x-3)(x-6)=0

We multiply parentheses ..

5(+x^2-6x-3x+18)=0

We multiply parentheses

5x^2-30x-15x+90=0

We add all the numbers together, and all the variables

5x^2-45x+90=0

a = 5; b = -45; c = +90;
Δ = b2-4ac
Δ = -452-4·5·90
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-15}{2*5}=\frac{30}{10}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15}{2*5}=\frac{60}{10}
=6
$