3(x-40)(x-6)=0

Solution for 3(x-40)(x-6)=0 equation:

3(x-40)(x-6)=0

We multiply parentheses ..

3(+x^2-6x-40x+240)=0

We multiply parentheses

3x^2-18x-120x+720=0

We add all the numbers together, and all the variables

3x^2-138x+720=0

a = 3; b = -138; c = +720;
Δ = b2-4ac
Δ = -1382-4·3·720
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-102}{2*3}=\frac{36}{6}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+102}{2*3}=\frac{240}{6}
=40
$