(3)(12x-15)(12x-21)=0

Solution for (3)(12x-15)(12x-21)=0 equation:

(3)(12x-15)(12x-21)=0

We multiply parentheses ..

3(+144x^2-252x-180x+315)=0

We multiply parentheses

432x^2-756x-540x+945=0

We add all the numbers together, and all the variables

432x^2-1296x+945=0

a = 432; b = -1296; c = +945;
Δ = b2-4ac
Δ = -12962-4·432·945
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1296)-216}{2*432}=\frac{1080}{864}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1296)+216}{2*432}=\frac{1512}{864}
=1+3/4
$